{"id":325464,"date":"2024-03-20T20:28:23","date_gmt":"2024-03-20T13:28:23","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=325464"},"modified":"2025-10-07T17:04:20","modified_gmt":"2025-10-07T10:04:20","slug":"hang-dang-thuc","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/hang-dang-thuc\/","title":{"rendered":"7 H\u1eb1ng \u0110\u1eb3ng Th\u1ee9c \u0110\u00e1ng Nh\u1edb: To\u00e0n t\u1eadp c\u00f4ng th\u1ee9c, v\u00ed d\u1ee5 &#038; b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng (To\u00e1n 8)"},"content":{"rendered":"<p data-sourcepos=\"3:1-3:263\"><strong>H\u1eb1ng \u0111\u1eb3ng th\u1ee9c<\/strong> l\u00e0 nh\u1eefng c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng th\u01b0\u1eddng xuy\u00ean, gi\u00fap ta gi\u1ea3i to\u00e1n nhanh ch\u00f3ng v\u00e0 ch\u00ednh x\u00e1c h\u01a1n. Trong ch\u01b0\u01a1ng tr\u00ecnh to\u00e1n h\u1ecdc THCS, c\u00f3 7 \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb \u0111\u00f3ng vai tr\u00f2 v\u00f4 c\u00f9ng quan tr\u1ecdng, \u0111\u01b0\u1ee3c xem l\u00e0 &#8220;ch\u00eca kh\u00f3a&#8221; \u0111\u1ec3 chinh ph\u1ee5c m\u00f4n \u0111\u1ea1i s\u1ed1 v\u00e0 7 \u0111\u1eb3ng th\u1ee9c n\u00e0y bao g\u1ed3m:<\/p>\n<ul data-sourcepos=\"7:1-14:0\">\n<li data-sourcepos=\"7:1-7:27\">B\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u<\/li>\n<li data-sourcepos=\"8:1-8:27\">B\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng<\/li>\n<li data-sourcepos=\"8:1-8:27\">Hi\u1ec7u hai b\u00ecnh ph\u01b0\u01a1ng<\/li>\n<li data-sourcepos=\"8:1-8:27\">L\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng<\/li>\n<li data-sourcepos=\"8:1-8:27\">L\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u<\/li>\n<li data-sourcepos=\"9:1-9:22\">T\u1ed5ng hai l\u1eadp ph\u01b0\u01a1ng<\/li>\n<li data-sourcepos=\"10:1-10:22\">Hi\u1ec7u hai l\u1eadp ph\u01b0\u01a1ng<\/li>\n<\/ul>\n<p data-sourcepos=\"21:1-21:240\">Trong b\u00e0i vi\u1ebft n\u00e0y, ch\u00fang ta c\u00f9ng kh\u00e1m ph\u00e1 chi ti\u1ebft v\u1ec1 t\u1eebng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c bao g\u1ed3m c\u00e1c c\u00f4ng th\u1ee9c, c\u00e1ch ch\u1ee9ng minh, v\u00ed d\u1ee5 minh h\u1ecda v\u00e0 b\u00e0i t\u1eadp \u00e1p d\u1ee5ng. Qua \u0111\u00f3, b\u1ea1n s\u1ebd n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c v\u00e0 c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng th\u00e0nh th\u1ea1o c\u00e1c \u0111\u1eb3ng th\u1ee9c n\u00e0y trong qu\u00e1 tr\u00ecnh h\u1ecdc t\u1eadp.<\/p>\n<h2>H\u1eb1ng \u0111\u1eb3ng th\u1ee9c l\u00e0 g\u00ec?<\/h2>\n<p>Trong to\u00e1n h\u1ecdc,\u00a0<strong>h\u1eb1ng \u0111\u1eb3ng th\u1ee9c<\/strong>\u00a0l\u00e0 m\u1ed9t \u0111\u1eb3ng th\u1ee9c (ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai v\u1ebf b\u1eb1ng nhau) lu\u00f4n \u0111\u00fang v\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb c\u1ee7a c\u00e1c bi\u1ebfn trong \u0111\u00f3. Ch\u00fang \u0111\u01b0\u1ee3c xem nh\u01b0 nh\u1eefng &#8220;c\u00f4ng th\u1ee9c v\u00e0ng&#8221; gi\u00fap \u0111\u01a1n gi\u1ea3n h\u00f3a vi\u1ec7c t\u00ednh to\u00e1n, khai tri\u1ec3n v\u00e0 ph\u00e2n t\u00edch c\u00e1c bi\u1ec3u th\u1ee9c \u0111\u1ea1i s\u1ed1 ph\u1ee9c t\u1ea1p.<\/p>\n<h2>T\u1ea1i sao 7 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c l\u1ea1i \u201c\u0111\u00e1ng nh\u1edb\u201d?<\/h2>\n<p>N\u1eafm v\u1eefng 7 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n l\u1edbp 8 l\u00e0 ch\u00eca kh\u00f3a gi\u00fap b\u1ea1n:<\/p>\n<ul>\n<li><strong>Gi\u1ea3i to\u00e1n nhanh h\u01a1n:<\/strong>\u00a0\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c \u0111\u1ec3 t\u00ednh nh\u1ea9m, r\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3.<\/li>\n<li><strong>Ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed:<\/strong>\u00a0\u0110\u00e2y l\u00e0 m\u1ed9t k\u1ef9 n\u0103ng n\u1ec1n t\u1ea3ng \u0111\u1ec3 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 nhi\u1ec1u b\u00e0i to\u00e1n ph\u1ee9c t\u1ea1p kh\u00e1c.<\/li>\n<li><strong>Ch\u1ee9ng minh \u0111\u1eb3ng th\u1ee9c v\u00e0 b\u1ea5t \u0111\u1eb3ng th\u1ee9c:<\/strong>\u00a0Bi\u1ebfn \u0111\u1ed5i c\u00e1c v\u1ebf c\u1ee7a bi\u1ec3u th\u1ee9c v\u1ec1 d\u1ea1ng quen thu\u1ed9c.<\/li>\n<li><strong>T\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t, nh\u1ecf nh\u1ea5t (GTLN, GTNN):<\/strong>\u00a0\u0110\u01b0a bi\u1ec3u th\u1ee9c v\u1ec1 d\u1ea1ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng\/hi\u1ec7u c\u1ed9ng v\u1edbi m\u1ed9t h\u1eb1ng s\u1ed1.<\/li>\n<\/ul>\n<h2>7 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb<\/h2>\n<p>Trong danh s\u00e1ch c\u00e1c c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc c\u1ea7n ghi nh\u1edb th\u00ec 7 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c ch\u00ednh l\u00e0 m\u1ed9t trong nh\u1eefng quy t\u1eafc m\u00e0 ch\u00fang ta c\u1ea7n n\u1eb1m l\u00f2ng. V\u1edbi nh\u1eefng b\u00e0i to\u00e1n kh\u00f3, nh\u1eefng b\u00e0i to\u00e1n v\u1edbi bi\u1ec3u th\u1ee9c d\u00e0i v\u00e0 bi\u1ebfn \u0111\u1ed5i th\u00ec nh\u1eefng \u0111\u1eb3ng th\u1ee9c n\u00e0y s\u1ebd gi\u00fap ch\u00fang ta g\u1ee1 r\u1ed1i, t\u1eeb \u0111\u00f3 c\u00f3 th\u1ec3 khi\u1ebfn \u0111\u1ed9 kh\u00f3 gi\u1ea3m \u0111i \u0111\u00f4i ch\u00fat v\u00e0 ch\u00fang ta c\u00f3 th\u1ec3 gi\u1ea3i quy\u1ebft nh\u1eefng b\u00e0i to\u00e1n m\u1ed9t c\u00e1ch d\u1ec5 d\u00e0ng h\u01a1n. Qua nh\u1eefng n\u1ed9i dung chi ti\u1ebft v\u1ec1 t\u1eebng \u0111\u1eb3ng th\u1ee9c trong n\u1ed9i dung ti\u1ebfp theo \u0111\u00e2y, h\u00e3y ghi ch\u00e9p v\u00e0 th\u1ef1c hi\u1ec7n nh\u1eefng b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng k\u00e8m theo \u0111\u1ec3 c\u00f3 th\u1ec3 n\u1eafm ch\u1eafc 7 \u0111\u1eb3ng th\u1ee9c trong tay nh\u00e9.<\/p>\n<h3>H\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u<\/h3>\n<p data-sourcepos=\"3:1-3:14\"><strong>1. C\u00f4ng th\u1ee9c H\u0110T b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u:\u00a0<\/strong><\/p>\n<p data-sourcepos=\"5:1-5:60\">B\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u hai s\u1ed1 <strong>a<\/strong> v\u00e0 <strong>b<\/strong> \u0111\u01b0\u1ee3c vi\u1ebft l\u00e0: (a &#8211; b)\u00b2 = a\u00b2 &#8211; 2ab + b\u00b2<\/p>\n<p data-sourcepos=\"9:1-9:20\"><strong>2. C\u00e1ch ch\u1ee9ng minh H\u0110T b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u<\/strong><\/p>\n<p data-sourcepos=\"11:1-11:40\"><em>C\u00e1ch 1: S\u1eed d\u1ee5ng khai tri\u1ec3n tr\u1ef1c ti\u1ebfp<\/em><\/p>\n<p data-sourcepos=\"13:1-13:25\">(a &#8211; b)\u00b2 = (a &#8211; b)(a &#8211; b)<\/p>\n<p data-sourcepos=\"15:1-15:19\">= a\u00b2 &#8211; ab &#8211; ab + b\u00b2<\/p>\n<p data-sourcepos=\"17:1-17:15\">= a\u00b2 &#8211; 2ab + b\u00b2<\/p>\n<p data-sourcepos=\"19:1-19:30\"><em>C\u00e1ch 2: S\u1eed d\u1ee5ng h\u00ecnh vu\u00f4ng<\/em><\/p>\n<p data-sourcepos=\"21:1-21:123\">V\u1ebd m\u1ed9t h\u00ecnh vu\u00f4ng c\u1ea1nh (a &#8211; b). Chia h\u00ecnh vu\u00f4ng th\u00e0nh 4 h\u00ecnh vu\u00f4ng nh\u1ecf, 1 h\u00ecnh vu\u00f4ng l\u1edbn c\u1ea1nh a v\u00e0 3 h\u00ecnh vu\u00f4ng nh\u1ecf c\u1ea1nh b.<\/p>\n<p data-sourcepos=\"23:1-23:37\">Di\u1ec7n t\u00edch h\u00ecnh vu\u00f4ng l\u1edbn l\u00e0: (a &#8211; b)\u00b2<\/p>\n<p data-sourcepos=\"25:1-25:48\">Di\u1ec7n t\u00edch 4 h\u00ecnh vu\u00f4ng nh\u1ecf l\u00e0: a\u00b2 + b\u00b2 + b\u00b2 + b\u00b2<\/p>\n<p data-sourcepos=\"27:1-27:41\">Suy ra: (a &#8211; b)\u00b2 = a\u00b2 + b\u00b2 + b\u00b2 + b\u00b2 &#8211; a\u00b2<\/p>\n<p data-sourcepos=\"29:1-29:15\">= a\u00b2 &#8211; 2ab + b\u00b2<\/p>\n<p data-sourcepos=\"29:1-29:15\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-5.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-5-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-5-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-325817 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-5.jpg\" alt=\"nhung-hang-dang-thuc-dang-nho-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p data-sourcepos=\"45:1-45:39\"><strong>3. B\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn c\u00f4ng th\u1ee9c H\u0110T b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u<\/strong><\/p>\n<p data-sourcepos=\"47:1-47:10\"><strong>B\u00e0i to\u00e1n 1: <\/strong>T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c: (x &#8211; 2)\u00b2 &#8211; (x &#8211; 3)\u00b2<\/p>\n<p data-sourcepos=\"53:1-53:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p data-sourcepos=\"55:1-55:51\">(x &#8211; 2)\u00b2 &#8211; (x &#8211; 3)\u00b2 = (x\u00b2 &#8211; 4x + 4) &#8211; (x\u00b2 &#8211; 6x + 9)<\/p>\n<p data-sourcepos=\"57:1-57:27\">= x\u00b2 &#8211; 4x + 4 &#8211; x\u00b2 + 6x &#8211; 9<\/p>\n<p data-sourcepos=\"59:1-59:9\">= 2x &#8211; 5<\/p>\n<p data-sourcepos=\"61:1-61:10\"><strong>B\u00e0i to\u00e1n 2: <\/strong>Ch\u1ee9ng minh r\u1eb1ng: (a &#8211; b)\u00b2 \u2265 0<\/p>\n<p data-sourcepos=\"67:1-67:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p data-sourcepos=\"69:1-69:24\">(a &#8211; b)\u00b2 = a\u00b2 &#8211; 2ab + b\u00b2<\/p>\n<p data-sourcepos=\"71:1-71:26\">= a\u00b2 &#8211; 2ab + b\u00b2 + 2ab &#8211; b\u00b2<\/p>\n<p data-sourcepos=\"73:1-73:21\">= (a &#8211; b)\u00b2 + 2ab &#8211; b\u00b2<\/p>\n<p data-sourcepos=\"75:1-75:50\">V\u00ec (a &#8211; b)\u00b2 lu\u00f4n l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 0 v\u1edbi m\u1ecdi a, b.<\/p>\n<p data-sourcepos=\"77:1-77:30\">Do \u0111\u00f3, (a &#8211; b)\u00b2 + 2ab &#8211; b\u00b2 \u2265 0<\/p>\n<p data-sourcepos=\"79:1-79:20\">Suy ra: (a &#8211; b)\u00b2 \u2265 0<\/p>\n<p data-sourcepos=\"81:1-81:10\"><strong>B\u00e0i to\u00e1n 3: <\/strong>T\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a x \u0111\u1ec3 bi\u1ec3u th\u1ee9c: Q = x\u00b2 &#8211; 8x + 17 \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t.<\/p>\n<p data-sourcepos=\"87:1-87:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p data-sourcepos=\"89:1-89:16\">Q = x\u00b2 &#8211; 8x + 17<\/p>\n<p data-sourcepos=\"91:1-91:20\">= (x\u00b2 &#8211; 8x + 16) + 1<\/p>\n<p data-sourcepos=\"93:1-93:14\">= (x &#8211; 4)\u00b2 + 1<\/p>\n<p data-sourcepos=\"95:1-95:47\">V\u00ec (x &#8211; 4)\u00b2 lu\u00f4n l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 0 v\u1edbi m\u1ecdi x.<\/p>\n<p data-sourcepos=\"97:1-97:49\">Do \u0111\u00f3, Q = (x &#8211; 4)\u00b2 + 1 lu\u00f4n l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 1.<\/p>\n<p data-sourcepos=\"99:1-99:25\">D\u1ea5u &#8220;=&#8221; x\u1ea3y ra khi x = 4.<\/p>\n<p data-sourcepos=\"101:1-101:42\">V\u1eady gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a Q l\u00e0 1 khi x = 4.<\/p>\n<h3>H\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng<\/h3>\n<p data-sourcepos=\"3:1-3:14\"><strong>1. C\u00f4ng th\u1ee9c H\u0110T b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng:\u00a0<\/strong><\/p>\n<p data-sourcepos=\"5:1-5:60\">B\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng hai s\u1ed1 <strong>a<\/strong> v\u00e0 <strong>b<\/strong> \u0111\u01b0\u1ee3c vi\u1ebft l\u00e0: <strong>(a + b)\u00b2 = a\u00b2 + 2ab + b\u00b2<\/strong><\/p>\n<p data-sourcepos=\"9:1-9:20\"><strong>2. C\u00e1ch ch\u1ee9ng minh H\u0110T b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng<\/strong><\/p>\n<p data-sourcepos=\"11:1-11:40\"><em>C\u00e1ch 1: S\u1eed d\u1ee5ng khai tri\u1ec3n tr\u1ef1c ti\u1ebfp<\/em><\/p>\n<p data-sourcepos=\"13:1-13:25\">(a + b)\u00b2 = (a + b)(a + b)<\/p>\n<p data-sourcepos=\"15:1-15:19\">= a\u00b2 + ab + ab + b\u00b2<\/p>\n<p data-sourcepos=\"17:1-17:15\">= a\u00b2 + 2ab + b\u00b2<\/p>\n<p data-sourcepos=\"19:1-19:30\"><em>C\u00e1ch 2: S\u1eed d\u1ee5ng h\u00ecnh vu\u00f4ng<\/em><\/p>\n<p data-sourcepos=\"21:1-21:99\">V\u1ebd m\u1ed9t h\u00ecnh vu\u00f4ng c\u1ea1nh (a + b). Chia h\u00ecnh vu\u00f4ng th\u00e0nh 4 h\u00ecnh vu\u00f4ng nh\u1ecf, m\u1ed7i h\u00ecnh vu\u00f4ng c\u1ea1nh a v\u00e0 b.<\/p>\n<p data-sourcepos=\"23:1-23:37\">Di\u1ec7n t\u00edch h\u00ecnh vu\u00f4ng l\u1edbn l\u00e0: (a + b)\u00b2<\/p>\n<p data-sourcepos=\"25:1-25:48\">Di\u1ec7n t\u00edch 4 h\u00ecnh vu\u00f4ng nh\u1ecf l\u00e0: a\u00b2 + a\u00b2 + b\u00b2 + b\u00b2<\/p>\n<p data-sourcepos=\"27:1-27:52\">Suy ra: (a + b)\u00b2 = a\u00b2 + a\u00b2 + b\u00b2 + b\u00b2 = a\u00b2 + 2ab + b\u00b2<\/p>\n<p data-sourcepos=\"27:1-27:52\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-6.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-6-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-6-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"alignnone size-full wp-image-325818 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-6.jpg\" alt=\"nhung-hang-dang-thuc-dang-nho-6\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p data-sourcepos=\"43:1-43:39\"><strong>3. B\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn c\u00f4ng th\u1ee9c H\u0110T b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng<\/strong><\/p>\n<p data-sourcepos=\"45:1-45:10\"><strong>B\u00e0i to\u00e1n 1: <\/strong>T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c: (x + 3)\u00b2 &#8211; (x &#8211; 2)\u00b2<\/p>\n<p data-sourcepos=\"51:1-51:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p data-sourcepos=\"53:1-53:51\">(x + 3)\u00b2 &#8211; (x &#8211; 2)\u00b2 = (x\u00b2 + 6x + 9) &#8211; (x\u00b2 &#8211; 4x + 4)<\/p>\n<p data-sourcepos=\"55:1-55:27\">= x\u00b2 + 6x + 9 &#8211; x\u00b2 + 4x &#8211; 4<\/p>\n<p data-sourcepos=\"57:1-57:9\">= 10x + 5<\/p>\n<p data-sourcepos=\"59:1-59:10\"><strong>B\u00e0i to\u00e1n 2: <\/strong>Ch\u1ee9ng minh r\u1eb1ng: (a + b)\u00b2 \u2265 4ab<\/p>\n<p data-sourcepos=\"65:1-65:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p data-sourcepos=\"67:1-67:36\">(a + b)\u00b2 &#8211; 4ab = a\u00b2 + 2ab + b\u00b2 &#8211; 4ab<\/p>\n<p data-sourcepos=\"69:1-69:15\">= a\u00b2 &#8211; 2ab + b\u00b2<\/p>\n<p data-sourcepos=\"71:1-71:14\">= (a &#8211; b)\u00b2 \u2265 0<\/p>\n<p data-sourcepos=\"73:1-73:50\">V\u00ec (a &#8211; b)\u00b2 lu\u00f4n l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 0 v\u1edbi m\u1ecdi a, b.<\/p>\n<p data-sourcepos=\"75:1-75:25\">Do \u0111\u00f3, (a + b)\u00b2 &#8211; 4ab \u2265 0<\/p>\n<p data-sourcepos=\"77:1-77:22\">Suy ra: (a + b)\u00b2 \u2265 4ab<\/p>\n<p data-sourcepos=\"79:1-79:10\"><strong>B\u00e0i to\u00e1n 3: <\/strong>T\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a x \u0111\u1ec3 bi\u1ec3u th\u1ee9c: P = x\u00b2 &#8211; 4x + 5 \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t.<\/p>\n<p data-sourcepos=\"85:1-85:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p data-sourcepos=\"87:1-87:15\">P = x\u00b2 &#8211; 4x + 5<\/p>\n<p data-sourcepos=\"89:1-89:19\">= (x\u00b2 &#8211; 4x + 4) + 1<\/p>\n<p data-sourcepos=\"91:1-91:14\">= (x &#8211; 2)\u00b2 + 1<\/p>\n<p data-sourcepos=\"93:1-93:47\">V\u00ec (x &#8211; 2)\u00b2 lu\u00f4n l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 0 v\u1edbi m\u1ecdi x.<\/p>\n<p data-sourcepos=\"95:1-95:49\">Do \u0111\u00f3, P = (x &#8211; 2)\u00b2 + 1 lu\u00f4n l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 1.<\/p>\n<p data-sourcepos=\"97:1-97:25\">D\u1ea5u &#8220;=&#8221; x\u1ea3y ra khi x = 2.<\/p>\n<p data-sourcepos=\"99:1-99:42\">V\u1eady gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a P l\u00e0 1 khi x = 2.<\/p>\n<h3 data-sourcepos=\"99:1-99:42\">H\u1eb1ng \u0111\u1eb3ng th\u1ee9c hi\u1ec7u hai b\u00ecnh ph\u01b0\u01a1ng<\/h3>\n<p data-sourcepos=\"3:1-3:14\"><strong>1. C\u00f4ng th\u1ee9c H\u0110T hi\u1ec7u hai b\u00ecnh ph\u01b0\u01a1ng:\u00a0<\/strong><\/p>\n<p>Hi\u1ec7u hai b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a hai s\u1ed1 <strong>a<\/strong> v\u00e0 <strong>b<\/strong> \u0111\u01b0\u1ee3c vi\u1ebft l\u00e0: a\u00b2 &#8211; b\u00b2 = (a &#8211; b)(a + b)<\/p>\n<p data-sourcepos=\"9:1-9:20\"><strong>2. C\u00e1ch ch\u1ee9ng minh H\u0110T hi\u1ec7u hai b\u00ecnh ph\u01b0\u01a1ng<\/strong><\/p>\n<p data-sourcepos=\"11:1-11:40\"><em>C\u00e1ch s\u1eed d\u1ee5ng khai tri\u1ec3n tr\u1ef1c ti\u1ebfp:<\/em><\/p>\n<p data-sourcepos=\"13:1-13:24\">a\u00b2 &#8211; b\u00b2 = (a + b)(a &#8211; b)<\/p>\n<p data-sourcepos=\"15:1-15:19\">= a\u00b2 + ab &#8211; ab &#8211; b\u00b2<\/p>\n<p data-sourcepos=\"17:1-17:15\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-3.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-3-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-3-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"alignnone size-full wp-image-325815 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-3.jpg\" alt=\"nhung-hang-dang-thuc-dang-nho-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p data-sourcepos=\"43:1-43:39\"><strong>3. B\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn c\u00f4ng th\u1ee9c H\u0110T hi\u1ec7u hai b\u00ecnh ph\u01b0\u01a1ng<\/strong><\/p>\n<p data-sourcepos=\"53:1-53:10\"><strong>B\u00e0i to\u00e1n 1: <\/strong>T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c: (x + 5)\u00b2 &#8211; (x &#8211; 2)\u00b2<\/p>\n<p data-sourcepos=\"59:1-59:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p data-sourcepos=\"59:1-59:9\">(x + 5)\u00b2 &#8211; (x &#8211; 2)\u00b2 = ((x + 5) &#8211; (x &#8211; 2))((x + 5) + (x &#8211; 2))<\/p>\n<p data-sourcepos=\"59:1-59:9\">= (x + 5 &#8211; x + 2)(x + 5 + x &#8211; 2)<\/p>\n<p data-sourcepos=\"59:1-59:9\">= 7(2x + 3)<\/p>\n<p data-sourcepos=\"59:1-59:9\">= 14x + 21<\/p>\n<p data-sourcepos=\"67:1-67:10\"><strong>B\u00e0i to\u00e1n 2: <\/strong>Ch\u1ee9ng minh r\u1eb1ng: (a + b)\u00b2 &#8211; (a &#8211; b)\u00b2 = 4ab<\/p>\n<p data-sourcepos=\"73:1-73:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p data-sourcepos=\"75:1-75:55\">(a + b)\u00b2 &#8211; (a &#8211; b)\u00b2 = ((a + b) &#8211; (a &#8211; b))((a + b) + (a &#8211; b))<\/p>\n<p data-sourcepos=\"75:1-75:55\">= (a\u00b2 + 2ab + b\u00b2) &#8211; (a\u00b2 &#8211; 2ab + b\u00b2)<\/p>\n<p data-sourcepos=\"77:1-77:31\">= a\u00b2 + 2ab + b\u00b2 &#8211; a\u00b2 + 2ab &#8211; b\u00b2<\/p>\n<p data-sourcepos=\"79:1-79:5\">= 4ab<\/p>\n<p data-sourcepos=\"81:1-81:10\"><strong>B\u00e0i to\u00e1n 3: <\/strong>T\u00ednh 56.64<\/p>\n<p data-sourcepos=\"87:1-87:9\"><strong>Gi\u1ea3i: <\/strong>Ta c\u00f3 56.64 = (60 &#8211; 4)(60 + 4) = 60\u00b2 &#8211; 4\u00b2 = 3600 &#8211; 16 = 3584<\/p>\n<p data-sourcepos=\"101:1-101:42\"><strong>B\u00e0i to\u00e1n 4:<\/strong> T\u00ednh (x &#8211; 2)(x + 2)<\/p>\n<p data-sourcepos=\"101:1-101:42\"><strong>Gi\u1ea3i:<\/strong> (x &#8211; 2)(x + 2) = x\u00b2 &#8211; 2\u00b2 = x\u00b2 &#8211; 4<\/p>\n<h3 data-sourcepos=\"101:1-101:42\">H\u1eb1ng \u0111\u1eb3ng th\u1ee9c l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng<\/h3>\n<p data-sourcepos=\"3:1-3:14\"><strong>1. C\u00f4ng th\u1ee9c H\u0110T l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng:\u00a0<\/strong><\/p>\n<p data-sourcepos=\"5:1-5:51\">L\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng hai s\u1ed1 <strong>a<\/strong> v\u00e0 <strong>b<\/strong> \u0111\u01b0\u1ee3c vi\u1ebft l\u00e0: (a + b)\u00b3 = a\u00b3 + 3a\u00b2b + 3ab\u00b2 + b\u00b3<\/p>\n<p data-sourcepos=\"9:1-9:20\"><strong>2. C\u00e1ch ch\u1ee9ng minh H\u0110T l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng<\/strong><\/p>\n<p data-sourcepos=\"11:1-11:40\"><em>C\u00e1ch s\u1eed d\u1ee5ng khai tri\u1ec3n tr\u1ef1c ti\u1ebfp<\/em><\/p>\n<p data-sourcepos=\"13:1-13:32\">(a + b)\u00b3 = (a + b)(a + b)(a + b)<\/p>\n<p data-sourcepos=\"15:1-15:33\">= a\u00b3 + a\u00b2b + a\u00b2b + ab\u00b2 + ab\u00b2 + b\u00b3<\/p>\n<p data-sourcepos=\"17:1-17:23\">= a\u00b3 + 3a\u00b2b + 3ab\u00b2 + b\u00b3<\/p>\n<p data-sourcepos=\"17:1-17:23\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-2.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-2-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-2-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-325814 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-2.jpg\" alt=\"nhung-hang-dang-thuc-dang-nho-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p data-sourcepos=\"43:1-43:39\"><strong>3. B\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn c\u00f4ng th\u1ee9c H\u0110T l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng<\/strong><\/p>\n<p data-sourcepos=\"47:1-47:10\"><strong>B\u00e0i to\u00e1n 1:<\/strong><\/p>\n<p data-sourcepos=\"49:1-49:27\">T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c: (x &#8211; 2)\u00b3 + (x + 1)\u00b3<\/p>\n<p data-sourcepos=\"53:1-53:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p data-sourcepos=\"55:1-55:64\">(x &#8211; 2)\u00b3 + (x + 1)\u00b3 = (x\u00b3 &#8211; 6x\u00b2 + 12x &#8211; 8) + (x\u00b3 + 3x\u00b2 + 3x + 1)<\/p>\n<p data-sourcepos=\"57:1-57:40\">= x\u00b3 &#8211; 6x\u00b2 + 12x &#8211; 8 + x\u00b3 + 3x\u00b2 + 3x + 1<\/p>\n<p data-sourcepos=\"59:1-59:21\">= 2x\u00b3 &#8211; 3x\u00b2 + 15x &#8211; 7<\/p>\n<p data-sourcepos=\"61:1-61:10\"><strong>B\u00e0i to\u00e1n 2: <\/strong>Ch\u1ee9ng minh r\u1eb1ng:<\/p>\n<p data-sourcepos=\"65:1-65:32\">(a + b)\u00b3 &#8211; a\u00b3 &#8211; b\u00b3 = 3a\u00b2b + 3ab\u00b2<\/p>\n<p data-sourcepos=\"67:1-67:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p data-sourcepos=\"69:1-69:54\">(a + b)\u00b3 &#8211; a\u00b3 &#8211; b\u00b3 = (a\u00b3 + 3a\u00b2b + 3ab\u00b2 + b\u00b3) &#8211; a\u00b3 &#8211; b\u00b3<\/p>\n<p data-sourcepos=\"71:1-71:33\">= a\u00b3 + 3a\u00b2b + 3ab\u00b2 + b\u00b3 &#8211; a\u00b3 &#8211; b\u00b3<\/p>\n<p data-sourcepos=\"73:1-73:13\">= 3a\u00b2b + 3ab\u00b2<\/p>\n<p><strong>B\u00e0i 3:<\/strong>\u00a0T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t (GTNN) c\u1ee7a bi\u1ec3u th\u1ee9c Q = x\u00b2 \u2013 8x + 17.<\/p>\n<p><strong>Gi\u1ea3i:<\/strong><\/p>\n<p>\u0110\u1ec3 t\u00ecm GTNN, ta s\u1ebd bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c v\u1ec1 d\u1ea1ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u:<\/p>\n<p>Q = x\u00b2 \u2013 8x + 17<\/p>\n<p>= (x\u00b2 \u2013 2.x.4 + 4\u00b2) + 1\u00a0<em>(T\u00e1ch 17 th\u00e0nh 16 + 1 \u0111\u1ec3 t\u1ea1o h\u1eb1ng \u0111\u1eb3ng th\u1ee9c)<\/em><\/p>\n<p>= (x \u2013 4)\u00b2 + 1<\/p>\n<p>V\u00ec (x \u2013 4)\u00b2 \u2265 0 v\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb c\u1ee7a x.<\/p>\n<p>Suy ra: (x \u2013 4)\u00b2 + 1 \u2265 1 v\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb c\u1ee7a x.<\/p>\n<p>V\u1eady GTNN c\u1ee7a Q l\u00e0 1. D\u1ea5u \u201c=\u201d x\u1ea3y ra khi x \u2013 4 = 0, t\u1ee9c l\u00e0 x = 4.<\/p>\n<h3 data-sourcepos=\"101:1-101:42\">H\u1eb1ng \u0111\u1eb3ng th\u1ee9c l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u<\/h3>\n<p data-sourcepos=\"3:1-3:14\"><strong>1. C\u00f4ng th\u1ee9c H\u0110T l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u:\u00a0<\/strong><\/p>\n<p data-sourcepos=\"3:1-3:14\"><strong>C\u00f4ng th\u1ee9c:<\/strong><\/p>\n<p data-sourcepos=\"5:1-5:51\">L\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u hai s\u1ed1 <strong>a<\/strong> v\u00e0 <strong>b<\/strong> \u0111\u01b0\u1ee3c vi\u1ebft l\u00e0: (a &#8211; b)\u00b3 = a\u00b3 &#8211; 3a\u00b2b + 3ab\u00b2 &#8211; b\u00b3<\/p>\n<p data-sourcepos=\"9:1-9:20\"><strong>2. C\u00e1ch ch\u1ee9ng minh H\u0110T l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u<\/strong><\/p>\n<p data-sourcepos=\"11:1-11:40\"><em>C\u00e1ch s\u1eed d\u1ee5ng khai tri\u1ec3n tr\u1ef1c ti\u1ebfp<\/em><\/p>\n<p data-sourcepos=\"13:1-13:32\">(a &#8211; b)\u00b3 = (a &#8211; b)(a &#8211; b)(a &#8211; b)<\/p>\n<p data-sourcepos=\"15:1-15:34\">= a\u00b3 &#8211; ab &#8211; ab + b\u00b2 &#8211; ab &#8211; b\u00b2 &#8211; b\u00b3<\/p>\n<p data-sourcepos=\"17:1-17:23\">= a\u00b3 &#8211; 3a\u00b2b + 3ab\u00b2 &#8211; b\u00b3<\/p>\n<p data-sourcepos=\"17:1-17:23\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-9.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-9-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-9-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-325812 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-9.jpg\" alt=\"nhung-hang-dang-thuc-dang-nho-9\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-9.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-9-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-9-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p data-sourcepos=\"43:1-43:39\"><strong>3. B\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn c\u00f4ng th\u1ee9c H\u0110T l\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u<\/strong><\/p>\n<p data-sourcepos=\"47:1-47:10\"><strong>B\u00e0i to\u00e1n 1: <\/strong>T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c: (x + 3)\u00b3 &#8211; (x &#8211; 2)\u00b3<\/p>\n<p data-sourcepos=\"53:1-53:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p data-sourcepos=\"55:1-55:66\">(x + 3)\u00b3 &#8211; (x &#8211; 2)\u00b3 = (x\u00b3 + 9x\u00b2 + 27x + 27) &#8211; (x\u00b3 &#8211; 6x\u00b2 + 12x &#8211; 8)<\/p>\n<p data-sourcepos=\"57:1-57:42\">= x\u00b3 + 9x\u00b2 + 27x + 27 &#8211; x\u00b3 + 6x\u00b2 &#8211; 12x + 8<\/p>\n<p data-sourcepos=\"59:1-59:17\">= 15x\u00b2 + 15x + 35<\/p>\n<p data-sourcepos=\"61:1-61:10\"><strong>B\u00e0i to\u00e1n 2: <\/strong>Ch\u1ee9ng minh r\u1eb1ng: (a &#8211; b)\u00b3 + a\u00b3 &#8211; b\u00b3 = 3a\u00b2b &#8211; 3ab\u00b2<\/p>\n<p data-sourcepos=\"67:1-67:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p data-sourcepos=\"69:1-69:54\">(a &#8211; b)\u00b3 + a\u00b3 &#8211; b\u00b3 = (a\u00b3 &#8211; 3a\u00b2b + 3ab\u00b2 &#8211; b\u00b3) + a\u00b3 &#8211; b\u00b3<\/p>\n<p data-sourcepos=\"71:1-71:33\">= a\u00b3 &#8211; 3a\u00b2b + 3ab\u00b2 &#8211; b\u00b3 + a\u00b3 &#8211; b\u00b3<\/p>\n<p data-sourcepos=\"73:1-73:13\">= 3a\u00b2b &#8211; 3ab\u00b2<\/p>\n<h3 data-sourcepos=\"101:1-101:42\">H\u1eb1ng \u0111\u1eb3ng th\u1ee9c t\u1ed5ng hai l\u1eadp ph\u01b0\u01a1ng<\/h3>\n<p data-sourcepos=\"3:1-3:14\"><strong>1. C\u00f4ng th\u1ee9c H\u0110T t\u1ed5ng hai l\u1eadp ph\u01b0\u01a1ng:\u00a0<\/strong><\/p>\n<p data-sourcepos=\"3:1-3:14\"><strong>C\u00f4ng th\u1ee9c:<\/strong><\/p>\n<p data-sourcepos=\"5:1-5:51\">T\u1ed5ng hai l\u1eadp ph\u01b0\u01a1ng c\u1ee7a hai s\u1ed1 <strong>a<\/strong> v\u00e0 <strong>b<\/strong> \u0111\u01b0\u1ee3c vi\u1ebft l\u00e0: a\u00b3 + b\u00b3 = (a + b)(a\u00b2 &#8211; ab + b\u00b2)<\/p>\n<p data-sourcepos=\"9:1-9:20\"><strong>2. C\u00e1ch ch\u1ee9ng minh H\u0110T t\u1ed5ng hai l\u1eadp ph\u01b0\u01a1ng<\/strong><\/p>\n<p data-sourcepos=\"11:1-11:40\"><em>C\u00e1ch s\u1eed d\u1ee5ng khai tri\u1ec3n tr\u1ef1c ti\u1ebfp<\/em><\/p>\n<p data-sourcepos=\"13:1-13:31\">a\u00b3 + b\u00b3 = (a + b)(a\u00b2 &#8211; ab + b\u00b2)<\/p>\n<p data-sourcepos=\"15:1-15:27\">= a\u00b3 + a\u00b2b &#8211; ab\u00b2 + ab\u00b2 + b\u00b3<\/p>\n<p data-sourcepos=\"17:1-17:9\">= a\u00b3 + b\u00b3<\/p>\n<p data-sourcepos=\"17:1-17:9\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-8.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-8-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-8-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-325811 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-8.jpg\" alt=\"nhung-hang-dang-thuc-dang-nho-8\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-8.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-8-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-8-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p data-sourcepos=\"43:1-43:39\"><strong>3. B\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn c\u00f4ng th\u1ee9c H\u0110T t\u1ed5ng hai l\u1eadp ph\u01b0\u01a1ng<\/strong><\/p>\n<p data-sourcepos=\"43:1-43:10\"><strong>B\u00e0i to\u00e1n 1:<\/strong><\/p>\n<p data-sourcepos=\"45:1-45:27\">T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c: (x &#8211; 1)\u00b3 + (x + 2)\u00b3<\/p>\n<p data-sourcepos=\"49:1-49:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p data-sourcepos=\"51:1-51:64\">(x &#8211; 1)\u00b3 + (x + 2)\u00b3 = (x\u00b3 &#8211; 3x\u00b2 + 3x &#8211; 1) + (x\u00b3 + 6x\u00b2 + 12x + 8)<\/p>\n<p data-sourcepos=\"53:1-53:40\">= x\u00b3 &#8211; 3x\u00b2 + 3x &#8211; 1 + x\u00b3 + 6x\u00b2 + 12x + 8<\/p>\n<p data-sourcepos=\"55:1-55:21\">= 2x\u00b3 + 3x\u00b2 + 15x + 7<\/p>\n<p data-sourcepos=\"57:1-57:10\"><strong>B\u00e0i 2: <\/strong>Ch\u1ee9ng minh r\u1eb1ng: a\u00b3 + b\u00b3 = (a + b)(a\u00b2 &#8211; ab + b\u00b2)<\/p>\n<p data-sourcepos=\"63:1-63:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p>Ta c\u00f3 th\u1ec3 ch\u1ee9ng minh h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u1eb1ng c\u00e1ch khai tri\u1ec3n v\u1ebf ph\u1ea3i (VP):<\/p>\n<p>VP = (a + b)(a\u00b2 \u2013 ab + b\u00b2)<\/p>\n<p>= a(a\u00b2 \u2013 ab + b\u00b2) + b(a\u00b2 \u2013 ab + b\u00b2)<\/p>\n<p>= (a\u00b3 \u2013 a\u00b2b + ab\u00b2) + (a\u00b2b \u2013 ab\u00b2 + b\u00b3)<\/p>\n<p>= a\u00b3 &#8211; a\u00b2b + a\u00b2b + ab\u00b2 &#8211; ab\u00b2 + b\u00b3<\/p>\n<p>= a\u00b3 + b\u00b3 = VT (V\u1ebf tr\u00e1i)<\/p>\n<p>V\u1eady \u0111\u1eb3ng th\u1ee9c \u0111\u00e3 \u0111\u01b0\u1ee3c ch\u1ee9ng minh.<\/p>\n<h3 data-sourcepos=\"101:1-101:42\">H\u1eb1ng \u0111\u1eb3ng th\u1ee9c hi\u1ec7u hai l\u1eadp ph\u01b0\u01a1ng<\/h3>\n<p data-sourcepos=\"3:1-3:14\"><strong>1. C\u00f4ng th\u1ee9c H\u0110T hi\u1ec7u hai l\u1eadp ph\u01b0\u01a1ng:\u00a0<\/strong><\/p>\n<p data-sourcepos=\"3:1-3:14\"><strong>C\u00f4ng th\u1ee9c: <\/strong>Hi\u1ec7u hai l\u1eadp ph\u01b0\u01a1ng c\u1ee7a hai s\u1ed1 <strong>a<\/strong> v\u00e0 <strong>b<\/strong> \u0111\u01b0\u1ee3c vi\u1ebft l\u00e0: <strong>a\u00b3 &#8211; b\u00b3 = (a &#8211; b)(a\u00b2 + ab + b\u00b2)<\/strong><\/p>\n<p data-sourcepos=\"9:1-9:20\"><strong>2. C\u00e1ch ch\u1ee9ng minh H\u0110T hi\u1ec7u hai l\u1eadp ph\u01b0\u01a1ng<\/strong><\/p>\n<p data-sourcepos=\"11:1-11:40\"><em>C\u00e1ch s\u1eed d\u1ee5ng khai tri\u1ec3n tr\u1ef1c ti\u1ebfp<\/em><\/p>\n<p data-sourcepos=\"13:1-13:31\">a\u00b3 &#8211; b\u00b3 = (a &#8211; b)(a\u00b2 + ab + b\u00b2)<\/p>\n<p data-sourcepos=\"15:1-15:29\">= a\u00b3 &#8211; ab &#8211; ab + b\u00b2 + ab + b\u00b3<\/p>\n<p data-sourcepos=\"17:1-17:9\">= a\u00b3 &#8211; b\u00b3<\/p>\n<p data-sourcepos=\"17:1-17:9\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-7.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-7-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-7-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-325810 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-7.jpg\" alt=\"nhung-hang-dang-thuc-dang-nho-7\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-7.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-7-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-7-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p data-sourcepos=\"43:1-43:39\"><strong>3. B\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn c\u00f4ng th\u1ee9c H\u0110T hi\u1ec7u hai l\u1eadp ph\u01b0\u01a1ng<\/strong><\/p>\n<p data-sourcepos=\"3:1-3:10\"><strong>B\u00e0i to\u00e1n 1: <\/strong>T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c: (x + 2)\u00b3 &#8211; (x &#8211; 1)\u00b3<\/p>\n<p data-sourcepos=\"9:1-9:9\"><strong>Gi\u1ea3i:<\/strong><\/p>\n<p data-sourcepos=\"11:1-11:64\">(x + 2)\u00b3 &#8211; (x &#8211; 1)\u00b3 = (x\u00b3 + 6x\u00b2 + 12x + 8) &#8211; (x\u00b3 &#8211; 3x\u00b2 + 3x &#8211; 1)<\/p>\n<p data-sourcepos=\"13:1-13:40\">= x\u00b3 + 6x\u00b2 + 12x + 8 &#8211; x\u00b3 + 3x\u00b2 &#8211; 3x + 1<\/p>\n<p data-sourcepos=\"15:1-15:14\">= 9x\u00b2 + 9x + 9<\/p>\n<p data-sourcepos=\"17:1-17:15\">= 9(x\u00b2 + x + 1)<\/p>\n<p data-sourcepos=\"19:1-19:10\"><strong>B\u00e0i to\u00e1n 2: <\/strong>Ch\u1ee9ng minh r\u1eb1ng: a\u00b3 &#8211; b\u00b3 = (a &#8211; b)(a\u00b2 + ab + b\u00b2)<\/p>\n<p data-sourcepos=\"25:1-25:11\"><strong>C\u00e1ch 1:<\/strong><\/p>\n<ul data-sourcepos=\"27:1-28:0\">\n<li data-sourcepos=\"27:1-28:0\">X\u00e9t a = 0 v\u00e0 b = 0, ta c\u00f3: 0\u00b3 &#8211; 0\u00b3 = (0 &#8211; 0)(0\u00b2 + 0.0 + 0\u00b2)<\/li>\n<\/ul>\n<p data-sourcepos=\"29:1-29:15\">=&gt; 0 = 0.0\u00b2 = 0<\/p>\n<ul data-sourcepos=\"31:1-32:0\">\n<li data-sourcepos=\"31:1-32:0\">X\u00e9t a = 1 v\u00e0 b = 1, ta c\u00f3: 1\u00b3 &#8211; 1\u00b3 = (1 &#8211; 1)(1\u00b2 + 1.1 + 1\u00b2)<\/li>\n<\/ul>\n<p data-sourcepos=\"33:1-33:15\">=&gt; 0 = 0.1\u00b2 = 0<\/p>\n<ul data-sourcepos=\"35:1-36:0\">\n<li data-sourcepos=\"35:1-36:0\">X\u00e9t a = -1 v\u00e0 b = -1, ta c\u00f3: (-1)\u00b3 &#8211; (-1)\u00b3 = (-1 &#8211; (-1))(-1\u00b2 &#8211; (-1).(-1) + (-1)\u00b2)<\/li>\n<\/ul>\n<p data-sourcepos=\"37:1-37:15\">=&gt; 0 = 0.1\u00b2 = 0<\/p>\n<ul data-sourcepos=\"39:1-40:0\">\n<li data-sourcepos=\"39:1-40:0\">X\u00e9t a = a v\u00e0 b = -a, ta c\u00f3: a\u00b3 &#8211; (-a)\u00b3 = (a &#8211; (-a))(a\u00b2 &#8211; a.(-a) + (-a)\u00b2)<\/li>\n<\/ul>\n<p data-sourcepos=\"41:1-41:20\">=&gt; 2a\u00b3 = 2a.a\u00b2 = 2a\u00b3<\/p>\n<p data-sourcepos=\"43:1-43:8\">=&gt; 0 = 0<\/p>\n<p data-sourcepos=\"45:1-45:61\">V\u00ec c\u00e1c tr\u01b0\u1eddng h\u1ee3p tr\u00ean \u0111\u1ec1u \u0111\u00fang, n\u00ean ta c\u00f3 th\u1ec3 k\u1ebft lu\u1eadn r\u1eb1ng:<\/p>\n<p data-sourcepos=\"47:1-47:31\">a\u00b3 &#8211; b\u00b3 = (a &#8211; b)(a\u00b2 + ab + b\u00b2)<\/p>\n<p data-sourcepos=\"49:1-49:11\"><strong>C\u00e1ch 2:<\/strong><\/p>\n<ul data-sourcepos=\"51:1-52:0\">\n<li data-sourcepos=\"51:1-52:0\">Ta c\u00f3: (a + b)(a &#8211; b) = a\u00b2 &#8211; ab + ab &#8211; b\u00b2<\/li>\n<\/ul>\n<p data-sourcepos=\"53:1-53:9\">= a\u00b2 &#8211; b\u00b2<\/p>\n<ul data-sourcepos=\"55:1-56:0\">\n<li data-sourcepos=\"55:1-56:0\">Thay b = -a, ta c\u00f3:<\/li>\n<\/ul>\n<p data-sourcepos=\"57:1-57:33\">(a + (-a))(a &#8211; (-a)) = a\u00b2 &#8211; (-a)\u00b2<\/p>\n<p data-sourcepos=\"59:1-59:9\">= a\u00b2 &#8211; a\u00b2<\/p>\n<p data-sourcepos=\"61:1-61:3\">= 0<\/p>\n<ul data-sourcepos=\"63:1-64:0\">\n<li data-sourcepos=\"63:1-64:0\">Do (a + b)(a &#8211; b) = a\u00b3 &#8211; b\u00b3, ta c\u00f3:<\/li>\n<\/ul>\n<p data-sourcepos=\"65:1-65:11\">a\u00b3 &#8211; b\u00b3 = 0<\/p>\n<p data-sourcepos=\"67:1-67:34\">=&gt; a\u00b3 &#8211; b\u00b3 = (a &#8211; b)(a\u00b2 + ab + b\u00b2)<\/p>\n<h2>C\u00e1c D\u1ea1ng B\u00e0i T\u1eadp \u1ee8ng D\u1ee5ng 7 H\u1eb1ng \u0110\u1eb3ng Th\u1ee9c Th\u01b0\u1eddng G\u1eb7p<\/h2>\n<p>Hi\u1ec3u l\u00fd thuy\u1ebft l\u00e0 m\u1ed9t chuy\u1ec7n, v\u1eadn d\u1ee5ng v\u00e0o gi\u1ea3i to\u00e1n l\u1ea1i l\u00e0 chuy\u1ec7n kh\u00e1c. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp \u0111i\u1ec3n h\u00ecnh m\u00e0 b\u1ea1n s\u1ebd g\u1eb7p:<\/p>\n<h4>D\u1ea1ng 1: T\u00ednh nhanh, t\u00ednh nh\u1ea9m<\/h4>\n<p><strong>V\u00ed d\u1ee5:<\/strong>\u00a0T\u00ednh 99\u00b2.<\/p>\n<p><strong>C\u00e1ch gi\u1ea3i:<\/strong>\u00a0Thay v\u00ec nh\u00e2n 99&#215;99, ta \u00e1p d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u:<\/p>\n<p>99\u00b2 = (100 &#8211; 1)\u00b2 = 100\u00b2 &#8211; 2.100.1 + 1\u00b2 = 10000 &#8211; 200 + 1 = 9801.<\/p>\n<h4>D\u1ea1ng 2: R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c<\/h4>\n<p><strong>V\u00ed d\u1ee5:<\/strong>\u00a0R\u00fat g\u1ecdn A = (x + y)\u00b2 &#8211; (x &#8211; y)\u00b2.<\/p>\n<p><strong>C\u00e1ch gi\u1ea3i:<\/strong>\u00a0\u00c1p d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c hi\u1ec7u hai b\u00ecnh ph\u01b0\u01a1ng a\u00b2 &#8211; b\u00b2 = (a-b)(a+b) v\u1edbi a = x+y v\u00e0 b = x-y.<\/p>\n<p>A = [(x + y) &#8211; (x &#8211; y)][(x + y) + (x &#8211; y)]<\/p>\n<p>A = [x + y &#8211; x + y][x + y + x &#8211; y]<\/p>\n<p>A = (2y)(2x) = 4xy.<\/p>\n<h4>D\u1ea1ng 3: Ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed<\/h4>\n<p><strong>V\u00ed d\u1ee5:<\/strong>\u00a0Ph\u00e2n t\u00edch 8x\u00b3 + 27 th\u00e0nh nh\u00e2n t\u1eed.<\/p>\n<p><strong>C\u00e1ch gi\u1ea3i:<\/strong>\u00a0Nh\u1eadn th\u1ea5y 8x\u00b3 = (2x)\u00b3 v\u00e0 27 = 3\u00b3. \u00c1p d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c t\u1ed5ng hai l\u1eadp ph\u01b0\u01a1ng a\u00b3 + b\u00b3 = (a+b)(a\u00b2-ab+b\u00b2).<\/p>\n<p>8x\u00b3 + 27 = (2x)\u00b3 + 3\u00b3 = (2x + 3)((2x)\u00b2 &#8211; 2x.3 + 3\u00b2) = (2x + 3)(4x\u00b2 &#8211; 6x + 9).<\/p>\n<h4>D\u1ea1ng 4: T\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t (GTLN), gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t (GTNN)<\/h4>\n<p><strong>V\u00ed d\u1ee5:<\/strong>\u00a0T\u00ecm GTNN c\u1ee7a bi\u1ec3u th\u1ee9c B = 4x\u00b2 + 4x + 5.<\/p>\n<p><strong>C\u00e1ch gi\u1ea3i:<\/strong>\u00a0Ta bi\u1ebfn \u0111\u1ed5i \u0111\u1ec3 xu\u1ea5t hi\u1ec7n b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng.<\/p>\n<p>B = (4x\u00b2 + 4x + 1) + 4 = (2x + 1)\u00b2 + 4.<\/p>\n<p>V\u00ec (2x + 1)\u00b2 \u2265 0 v\u1edbi m\u1ecdi x, n\u00ean B = (2x + 1)\u00b2 + 4 \u2265 4.<\/p>\n<p>GTNN c\u1ee7a B l\u00e0 4, \u0111\u1ea1t \u0111\u01b0\u1ee3c khi 2x + 1 = 0 \u21d4 x = -1\/2.<\/p>\n<h2 data-sourcepos=\"67:1-67:34\">\u1ee8ng d\u1ee5ng c\u1ee7a 7 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb<\/h2>\n<p data-sourcepos=\"67:1-67:34\">V\u1edbi nh\u1eefng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb ta c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng khi gi\u1ea3i m\u1ed9t s\u1ed1 d\u1ea1ng b\u00e0i t\u1eadp to\u00e1n nh\u01b0 sau:<\/p>\n<ul>\n<li data-sourcepos=\"67:1-67:34\">\u00c1p d\u1ee5ng tr\u1ef1c ti\u1ebfp b\u1eb1ng c\u00e1c h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u1ec3 th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh, t\u00ednh gi\u00e1 tr\u1ecb c\u00e1c bi\u1ec3u th\u1ee9c s\u1ed1.<\/li>\n<li data-sourcepos=\"67:1-67:34\">\u00c1p d\u1ee5ng c\u00e1c h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u1ec3 thu g\u1ecdn bi\u1ec3u th\u1ee9c v\u00e0 ch\u1ee9ng minh c\u00e1c \u0111\u1eb3ng th\u1ee9c.<\/li>\n<li data-sourcepos=\"67:1-67:34\">\u00c1p d\u1ee5ng c\u00e1c h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u1ec3 gi\u1ea3i b\u00e0i to\u00e1n t\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn v\u00e0 x\u00e1c \u0111\u1ecbnh h\u1ec7 s\u1ed1 c\u1ee7a \u0111a th\u1ee9c.<\/li>\n<li data-sourcepos=\"67:1-67:34\">\u00c1p d\u1ee5ng \u0111\u1ec3 t\u00ednh to\u00e1n c\u00e1c gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c v\u1edbi c\u00e1c bi\u1ebfn c\u00f3 \u0111i\u1ec1u ki\u1ec7n.<\/li>\n<li data-sourcepos=\"67:1-67:34\">Ch\u1ee9ng minh b\u1ea5t \u0111\u1eb3ng th\u1ee9c v\u00e0 b\u00e0i to\u00e1n t\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t, gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c \u0111\u1ea1i s\u1ed1.<\/li>\n<li data-sourcepos=\"67:1-67:34\">\u00c1p d\u1ee5ng c\u00e1c h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u1ec3 gi\u1ea3i m\u1ed9t s\u1ed1 b\u00e0i to\u00e1n s\u1ed1 h\u1ecdc v\u00e0 t\u1ed5 h\u1ee3p.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-4.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-4-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/03\/hang-dang-thuc-4-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-325816 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-4.jpg\" alt=\"nhung-hang-dang-thuc-dang-nho-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/03\/hang-dang-thuc-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h2>T\u1ea1m k\u1ebft<\/h2>\n<p data-sourcepos=\"69:1-69:200\">H\u1eb1ng \u0111\u1eb3ng th\u1ee9c l\u00e0 c\u00f4ng c\u1ee5 quan tr\u1ecdng gi\u00fap ta gi\u1ea3i to\u00e1n nhanh ch\u00f3ng v\u00e0 ch\u00ednh x\u00e1c. Vi\u1ec7c n\u1eafm v\u1eefng v\u00e0 s\u1eed d\u1ee5ng th\u00e0nh th\u1ea1o c\u00e1c \u0111\u1eb3ng th\u1ee9c s\u1ebd gi\u00fap b\u1ea1n h\u1ecdc t\u1eadp hi\u1ec7u qu\u1ea3 h\u01a1n khi nh\u1eefng b\u00e0i to\u00e1n s\u1ebd b\u1ecb &#8220;h\u1ea1 \u0111o v\u00e1n&#8221; m\u1ed9t c\u00e1ch thu\u1ea7n th\u1ee5c. Qua n\u1ed9i dung t\u1ed5ng h\u1ee3p tr\u00ean c\u1ee7a <a href=\"https:\/\/hoanghamobile.com\/\">Ho\u00e0ng H\u00e0 Mobile<\/a>, hy v\u1ecdng b\u1ea1n \u0111\u1ecdc \u0111\u00e3 k\u1ecbp ghi nh\u1edb v\u00e0 s\u1eed d\u1ee5ng th\u00e0nh t\u1ea1o c\u00e1c quy t\u1eafc t\u00ednh to\u00e1n n\u00e0y. \u0110\u00e2y \u0111\u01b0\u1ee3c xem l\u00e0 m\u1ed9t ph\u1ea7n ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n c\u1ea7n n\u1eafm v\u1eefng, v\u00ec v\u1eady h\u00e3y c\u1ed1 g\u1eafng nh\u1edb h\u1ebft t\u1ea5t c\u1ea3 nh\u00e9!<\/p>\n<p>XEM TH\u00caM:<\/p>\n<ul>\n<li><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-hinh-binh-hanh\/\">C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh ch\u00ednh x\u00e1c nh\u1ea5t 2023 v\u00e0 b\u00e0i t\u1eadp<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/trong-tam-la-gi\/\">T\u00ednh ch\u1ea5t c\u1ee7a tr\u1ecdng t\u00e2m v\u00e0 c\u00e1ch x\u00e1c \u0111\u1ecbnh tr\u1ecdng t\u00e2m tam gi\u00e1c trong H\u00ecnh h\u1ecdc<\/a><\/strong><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>H\u1eb1ng \u0111\u1eb3ng th\u1ee9c l\u00e0 nh\u1eefng c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng th\u01b0\u1eddng xuy\u00ean, gi\u00fap ta gi\u1ea3i to\u00e1n nhanh ch\u00f3ng v\u00e0 ch\u00ednh x\u00e1c h\u01a1n. Trong ch\u01b0\u01a1ng tr\u00ecnh to\u00e1n h\u1ecdc THCS, c\u00f3 7 \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb \u0111\u00f3ng vai tr\u00f2 v\u00f4 c\u00f9ng quan tr\u1ecdng, \u0111\u01b0\u1ee3c xem l\u00e0 &#8220;ch\u00eca kh\u00f3a&#8221; \u0111\u1ec3 chinh ph\u1ee5c m\u00f4n \u0111\u1ea1i s\u1ed1 v\u00e0 [&hellip;]<\/p>\n","protected":false},"author":75,"featured_media":325819,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-325464","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v24.2 (Yoast SEO v24.2) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>T\u1ed5ng H\u1ee3p 7 H\u1eb1ng \u0110\u1eb3ng Th\u1ee9c \u0110\u00e1ng Nh\u1edb (L\u1edbp 8): C\u00f4ng Th\u1ee9c &amp; B\u00e0i T\u1eadp C\u00f3 L\u1eddi Gi\u1ea3i<\/title>\n<meta name=\"description\" content=\"N\u1eafm v\u1eefng 7 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao. 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