{"id":567228,"date":"2026-07-20T11:49:41","date_gmt":"2026-07-20T04:49:41","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=567228"},"modified":"2026-07-21T14:59:32","modified_gmt":"2026-07-21T07:59:32","slug":"bat-phuong-trinh","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/bat-phuong-trinh\/","title":{"rendered":"B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 g\u00ec? C\u00e1ch gi\u1ea3i v\u00e0 v\u00ed d\u1ee5 chi ti\u1ebft"},"content":{"rendered":"<p>B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 ch\u1ee9a \u1ea9n, trong \u0111\u00f3 hai v\u1ebf \u0111\u01b0\u1ee3c n\u1ed1i v\u1edbi nhau b\u1eb1ng m\u1ed9t trong c\u00e1c d\u1ea5u b\u1ea5t \u0111\u1eb3ng th\u1ee9c: l\u1edbn h\u01a1n (&gt;), nh\u1ecf h\u01a1n (&lt;), l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng (\u2265), nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng (\u2264). V\u00ed d\u1ee5 2x + 1 &gt; 5 l\u00e0 m\u1ed9t b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh. Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 t\u00ecm t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a \u1ea9n l\u00e0m cho b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00fang. \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c quan tr\u1ecdng c\u1ee7a \u0110\u1ea1i s\u1ed1. B\u00e0i vi\u1ebft n\u00e0y tr\u00ecnh b\u00e0y \u0111\u1ecbnh ngh\u0129a, c\u00e1c quy t\u1eafc bi\u1ebfn \u0111\u1ed5i v\u00e0 c\u00e1ch gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t, b\u1eadc hai m\u1ed9t \u1ea9n c\u00f9ng d\u1ea1ng ch\u1ee9a \u1ea9n \u1edf m\u1eabu, k\u00e8m v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft t\u1eebng b\u01b0\u1edbc.<\/p>\n<h2>B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 g\u00ec?<\/h2>\n<p>B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh m\u1ed9t \u1ea9n l\u00e0 m\u1ec7nh \u0111\u1ec1 ch\u1ee9a \u1ea9n c\u00f3 d\u1ea1ng f(x) &gt; g(x) (ho\u1eb7c f(x) &lt; g(x), f(x) \u2265 g(x), f(x) \u2264 g(x)), trong \u0111\u00f3 f(x) v\u00e0 g(x) l\u00e0 c\u00e1c bi\u1ec3u th\u1ee9c c\u1ee7a \u1ea9n x. Gi\u00e1 tr\u1ecb c\u1ee7a \u1ea9n l\u00e0m cho b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh tr\u1edf th\u00e0nh m\u1ec7nh \u0111\u1ec1 \u0111\u00fang \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 m\u1ed9t nghi\u1ec7m; t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c nghi\u1ec7m g\u1ecdi l\u00e0 t\u1eadp nghi\u1ec7m. Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh l\u00e0 t\u00ecm t\u1eadp nghi\u1ec7m c\u1ee7a n\u00f3.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-567756 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-1.jpg\" alt=\"bat-phuong-trinh-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e1c quy t\u1eafc bi\u1ebfn \u0111\u1ed5i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh<\/h2>\n<p>\u0110\u1ec3 gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh, ta d\u00f9ng c\u00e1c quy t\u1eafc bi\u1ebfn \u0111\u1ed5i t\u01b0\u01a1ng \u0111\u01b0\u01a1ng sau:<\/p>\n<ul>\n<li>Quy t\u1eafc chuy\u1ec3n v\u1ebf: khi chuy\u1ec3n m\u1ed9t h\u1ea1ng t\u1eed t\u1eeb v\u1ebf n\u00e0y sang v\u1ebf kia, ta ph\u1ea3i \u0111\u1ed5i d\u1ea5u h\u1ea1ng t\u1eed \u0111\u00f3 (gi\u1ed1ng nh\u01b0 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh).<\/li>\n<li>Quy t\u1eafc nh\u00e2n (chia) v\u1edbi s\u1ed1 d\u01b0\u01a1ng: nh\u00e2n ho\u1eb7c chia c\u1ea3 hai v\u1ebf v\u1edbi c\u00f9ng m\u1ed9t s\u1ed1 d\u01b0\u01a1ng th\u00ec gi\u1eef nguy\u00ean chi\u1ec1u b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh.<\/li>\n<li>Quy t\u1eafc nh\u00e2n (chia) v\u1edbi s\u1ed1 \u00e2m: nh\u00e2n ho\u1eb7c chia c\u1ea3 hai v\u1ebf v\u1edbi c\u00f9ng m\u1ed9t s\u1ed1 \u00e2m th\u00ec ph\u1ea3i \u0111\u1ed5i chi\u1ec1u b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh.<\/li>\n<\/ul>\n<p>Quy t\u1eafc th\u1ee9 ba l\u00e0 \u0111i\u1ec3m kh\u00e1c bi\u1ec7t quan tr\u1ecdng nh\u1ea5t so v\u1edbi gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh \u2013 r\u1ea5t nhi\u1ec1u h\u1ecdc sinh qu\u00ean \u0111\u1ed5i chi\u1ec1u khi nh\u00e2n\/chia v\u1edbi s\u1ed1 \u00e2m.<\/p>\n<p><strong>Xem th\u00eam: <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/tiep-tuyen-la-gi\/\">Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1<\/a><\/strong><\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-567757 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-2.jpg\" alt=\"bat-phuong-trinh-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e1ch gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t m\u1ed9t \u1ea9n<\/h2>\n<p>B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t m\u1ed9t \u1ea9n c\u00f3 d\u1ea1ng ax + b &gt; 0 (ho\u1eb7c &lt;, \u2265, \u2264) v\u1edbi a \u2260 0. C\u00e1ch gi\u1ea3i:<\/p>\n<ul>\n<li>B\u01b0\u1edbc 1: Chuy\u1ec3n c\u00e1c h\u1ea1ng t\u1eed ch\u1ee9a \u1ea9n v\u1ec1 m\u1ed9t v\u1ebf, h\u1eb1ng s\u1ed1 v\u1ec1 v\u1ebf kia.<\/li>\n<li>B\u01b0\u1edbc 2: R\u00fat g\u1ecdn \u0111\u1ec3 \u0111\u01b0a v\u1ec1 d\u1ea1ng ax &gt; c (ho\u1eb7c d\u1ea1ng t\u01b0\u01a1ng \u1ee9ng).<\/li>\n<li>B\u01b0\u1edbc 3: Chia hai v\u1ebf cho a; n\u1ebfu a &gt; 0 gi\u1eef nguy\u00ean chi\u1ec1u, n\u1ebfu a &lt; 0 th\u00ec \u0111\u1ed5i chi\u1ec1u.<\/li>\n<li>B\u01b0\u1edbc 4: K\u1ebft lu\u1eadn t\u1eadp nghi\u1ec7m.<\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"size-full wp-image-567758 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-3.jpg\" alt=\"bat-phuong-trinh-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>V\u00ed d\u1ee5 gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t m\u1ed9t \u1ea9n<\/h2>\n<ul>\n<li><strong>V\u00ed d\u1ee5 1:<\/strong> Gi\u1ea3i 2x + 1 &gt; 5. Chuy\u1ec3n v\u1ebf: 2x &gt; 4. Chia 2 (s\u1ed1 d\u01b0\u01a1ng, gi\u1eef chi\u1ec1u): x &gt; 2. T\u1eadp nghi\u1ec7m l\u00e0 {x | x &gt; 2}.<\/li>\n<li><strong>V\u00ed d\u1ee5 2:<\/strong> Gi\u1ea3i \u22123x + 6 \u2265 0. Chuy\u1ec3n v\u1ebf: \u22123x \u2265 \u22126. Chia \u22123 (s\u1ed1 \u00e2m, \u0111\u1ed5i chi\u1ec1u): x \u2264 2. T\u1eadp nghi\u1ec7m {x | x \u2264 2}.<\/li>\n<li><strong>V\u00ed d\u1ee5 3:<\/strong> Gi\u1ea3i 5x \u2212 2 &lt; 3x + 4. Chuy\u1ec3n v\u1ebf: 2x &lt; 6, suy ra x &lt; 3.<\/li>\n<\/ul>\n<p><strong>Xem th\u00eam: <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/delta-delta-phay\/\">N\u1eafm V\u1eefng C\u00f4ng Th\u1ee9c Delta ; Delta Ph\u1ea9y: Ch\u00eca Kh\u00f3a Gi\u1ea3i Ph\u01b0\u01a1ng Tr\u00ecnh B\u1eadc Hai<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-567759 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-4.jpg\" alt=\"bat-phuong-trinh-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/bat-phuong-trinh-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e1ch gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai m\u1ed9t \u1ea9n<\/h2>\n<p>B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai m\u1ed9t \u1ea9n c\u00f3 d\u1ea1ng ax\u00b2 + bx + c &gt; 0 (ho\u1eb7c &lt;, \u2265, \u2264) v\u1edbi a \u2260 0, v\u00e0 c\u00e1ch gi\u1ea3i l\u00e0 x\u00e9t d\u1ea5u c\u1ee7a tam th\u1ee9c b\u1eadc hai f(x) = ax\u00b2 + bx + c.<\/p>\n<p>\u0110\u1eb7t \u0394 = b\u00b2 \u2212 4ac; d\u1ea5u c\u1ee7a f(x) x\u00e1c \u0111\u1ecbnh theo \u0111\u1ecbnh l\u00fd d\u1ea5u tam th\u1ee9c b\u1eadc hai sau:<\/p>\n<table>\n<thead>\n<tr>\n<th>Tr\u01b0\u1eddng h\u1ee3p<\/th>\n<th>D\u1ea5u c\u1ee7a f(x) = ax\u00b2 + bx + c<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0394 &lt; 0<\/td>\n<td>f(x) c\u00f9ng d\u1ea5u v\u1edbi h\u1ec7 s\u1ed1 a, v\u1edbi m\u1ecdi x \u2208 R<\/td>\n<\/tr>\n<tr>\n<td>\u0394 = 0<\/td>\n<td>f(x) c\u00f9ng d\u1ea5u v\u1edbi h\u1ec7 s\u1ed1 a, v\u1edbi m\u1ecdi x \u2260 \u2212b\/2a (t\u1ea1i x = \u2212b\/2a th\u00ec f(x) = 0)<\/td>\n<\/tr>\n<tr>\n<td>\u0394 &gt; 0 (c\u00f3 2 nghi\u1ec7m x1 &lt; x2)<\/td>\n<td>f(x) c\u00f9ng d\u1ea5u v\u1edbi a khi x &lt; x1 ho\u1eb7c x &gt; x2; tr\u00e1i d\u1ea5u v\u1edbi a khi x1 &lt; x &lt; x2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>C\u00e1c b\u01b0\u1edbc gi\u1ea3i:<\/p>\n<ul>\n<li>B\u01b0\u1edbc 1: Chuy\u1ec3n b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 d\u1ea1ng f(x) so v\u1edbi 0.<\/li>\n<li>B\u01b0\u1edbc 2: T\u00ednh \u0394 = b\u00b2 \u2212 4ac, t\u00ecm nghi\u1ec7m f(x) = 0 (n\u1ebfu c\u00f3).<\/li>\n<li>B\u01b0\u1edbc 3: X\u00e9t d\u1ea5u f(x) theo b\u1ea3ng tr\u00ean, d\u1ef1a v\u00e0o d\u1ea5u h\u1ec7 s\u1ed1 a.<\/li>\n<li>B\u01b0\u1edbc 4: \u0110\u1ed1i chi\u1ebfu chi\u1ec1u b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh ban \u0111\u1ea7u \u0111\u1ec3 k\u1ebft lu\u1eadn t\u1eadp nghi\u1ec7m.<\/li>\n<\/ul>\n<p>V\u00ed d\u1ee5: x\u00e9t b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh x\u00b2 \u2212 5x + 6 \u2265 0. Ta c\u00f3 a = 1, b = \u22125, c = 6 n\u00ean \u0394 = 25 \u2212 24 = 1 &gt; 0, ph\u01b0\u01a1ng tr\u00ecnh x\u00b2 \u2212 5x + 6 = 0 c\u00f3 hai nghi\u1ec7m x1 = 2 v\u00e0 x2 = 3. V\u00ec a = 1 &gt; 0, f(x) c\u00f9ng d\u1ea5u a (d\u01b0\u01a1ng) khi x &lt; 2 ho\u1eb7c x &gt; 3, v\u00e0 tr\u00e1i d\u1ea5u a (\u00e2m) khi 2 &lt; x &lt; 3. B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh y\u00eau c\u1ea7u f(x) \u2265 0 n\u00ean t\u1eadp nghi\u1ec7m l\u00e0 S = (\u2212\u221e; 2] \u222a [3; +\u221e).<\/p>\n<h2>C\u00e1ch gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a \u1ea9n \u1edf m\u1eabu<\/h2>\n<p>B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a \u1ea9n \u1edf m\u1eabu c\u00f3 \u1ea9n x n\u1eb1m \u1edf m\u1eabu th\u1ee9c; c\u00e1ch gi\u1ea3i l\u00e0 \u0111\u01b0a v\u1ec1 d\u1ea1ng so s\u00e1nh m\u1ed9t ph\u00e2n th\u1ee9c v\u1edbi 0 r\u1ed3i l\u1eadp b\u1ea3ng x\u00e9t d\u1ea5u, thay v\u00ec quy \u0111\u1ed3ng kh\u1eed m\u1eabu nh\u01b0 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh.<\/p>\n<p>C\u00e1c b\u01b0\u1edbc gi\u1ea3i:<\/p>\n<ul>\n<li>B\u01b0\u1edbc 1: Chuy\u1ec3n v\u1ebf, quy \u0111\u1ed3ng \u0111\u1ec3 \u0111\u01b0a v\u1ec1 d\u1ea1ng P(x)\/Q(x) so v\u1edbi 0.<\/li>\n<li>B\u01b0\u1edbc 2: T\u00ecm nghi\u1ec7m P(x) = 0 v\u00e0 Q(x) = 0; gi\u00e1 tr\u1ecb l\u00e0m Q(x) = 0 lu\u00f4n b\u1ecb lo\u1ea1i kh\u1ecfi t\u1eadp nghi\u1ec7m, k\u1ec3 c\u1ea3 khi b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 d\u1ea5u \u2265 ho\u1eb7c \u2264.<\/li>\n<li>B\u01b0\u1edbc 3: L\u1eadp b\u1ea3ng x\u00e9t d\u1ea5u c\u1ee7a P(x) v\u00e0 Q(x) tr\u00ean t\u1eebng kho\u1ea3ng.<\/li>\n<li>B\u01b0\u1edbc 4: Suy ra d\u1ea5u c\u1ee7a P(x)\/Q(x), \u0111\u1ed1i chi\u1ebfu chi\u1ec1u b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 k\u1ebft lu\u1eadn t\u1eadp nghi\u1ec7m.<\/li>\n<\/ul>\n<p>V\u00ed d\u1ee5: x\u00e9t b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh (2x \u2212 4)\/(x + 1) \u2265 0, \u0111i\u1ec1u ki\u1ec7n x \u2260 \u22121. T\u1eed s\u1ed1 2x \u2212 4 = 0 khi x = 2; m\u1eabu s\u1ed1 x + 1 = 0 khi x = \u22121. B\u1ea3ng x\u00e9t d\u1ea5u:<\/p>\n<table>\n<thead>\n<tr>\n<th>Kho\u1ea3ng c\u1ee7a x<\/th>\n<th>D\u1ea5u c\u1ee7a 2x \u2212 4<\/th>\n<th>D\u1ea5u c\u1ee7a x + 1<\/th>\n<th>D\u1ea5u c\u1ee7a (2x \u2212 4)\/(x + 1)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>x &lt; \u22121<\/td>\n<td>\u2212<\/td>\n<td>\u2212<\/td>\n<td>+<\/td>\n<\/tr>\n<tr>\n<td>\u22121 &lt; x &lt; 2<\/td>\n<td>\u2212<\/td>\n<td>+<\/td>\n<td>\u2212<\/td>\n<\/tr>\n<tr>\n<td>x &gt; 2<\/td>\n<td>+<\/td>\n<td>+<\/td>\n<td>+<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>T\u1ea1i x = 2, f(x) = 0 n\u00ean th\u1ecfa \u0111i\u1ec1u ki\u1ec7n \u2265 0 v\u00e0 \u0111\u01b0\u1ee3c l\u1ea5y v\u00e0o t\u1eadp nghi\u1ec7m; x = \u22121 l\u00e0m m\u1eabu b\u1eb1ng 0 n\u00ean lu\u00f4n b\u1ecb lo\u1ea1i. V\u1eady f(x) \u2265 0 khi x &lt; \u22121 ho\u1eb7c x \u2265 2, t\u1eadp nghi\u1ec7m l\u00e0 S = (\u2212\u221e; \u22121) \u222a [2; +\u221e).<\/p>\n<h2>Bi\u1ec3u di\u1ec5n t\u1eadp nghi\u1ec7m tr\u00ean tr\u1ee5c s\u1ed1<\/h2>\n<p>Sau khi gi\u1ea3i, t\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh th\u01b0\u1eddng \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n tr\u00ean tr\u1ee5c s\u1ed1 \u0111\u1ec3 d\u1ec5 h\u00ecnh dung. V\u1edbi x &gt; 2, ta g\u1ea1ch b\u1ecf ph\u1ea7n b\u00ean tr\u00e1i \u0111i\u1ec3m 2 v\u00e0 d\u00f9ng d\u1ea5u ngo\u1eb7c tr\u00f2n t\u1ea1i \u0111i\u1ec3m 2 (kh\u00f4ng l\u1ea5y gi\u00e1 tr\u1ecb 2). V\u1edbi x \u2264 2, ta d\u00f9ng d\u1ea5u ngo\u1eb7c vu\u00f4ng (l\u1ea5y c\u1ea3 \u0111i\u1ec3m 2) v\u00e0 bi\u1ec3u di\u1ec5n ph\u1ea7n b\u00ean tr\u00e1i. C\u00e1ch bi\u1ec3u di\u1ec5n n\u00e0y gi\u00fap ki\u1ec3m tra v\u00e0 tr\u00ecnh b\u00e0y nghi\u1ec7m r\u00f5 r\u00e0ng.<\/p>\n<p>T\u1eadp nghi\u1ec7m c\u0169ng c\u00f3 th\u1ec3 vi\u1ebft b\u1eb1ng k\u00fd hi\u1ec7u kho\u1ea3ng: (a; b) kh\u00f4ng l\u1ea5y hai \u0111\u1ea7u m\u00fat, \u0111o\u1ea1n [a; b] l\u1ea5y c\u1ea3 hai \u0111\u1ea7u m\u00fat, n\u1eeda kho\u1ea3ng (a; b] ho\u1eb7c [a; b) ch\u1ec9 l\u1ea5y m\u1ed9t \u0111\u1ea7u; nhi\u1ec1u kho\u1ea3ng t\u00e1ch r\u1eddi th\u00ec n\u1ed1i b\u1eb1ng k\u00fd hi\u1ec7u h\u1ee3p \u222a, v\u00ed d\u1ee5 S = (\u2212\u221e; 2] \u222a [3; +\u221e).<\/p>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh<\/h2>\n<h3>B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 g\u00ec?<\/h3>\n<p>L\u00e0 m\u1ec7nh \u0111\u1ec1 ch\u1ee9a \u1ea9n n\u1ed1i hai v\u1ebf b\u1eb1ng d\u1ea5u &gt;, &lt;, \u2265 ho\u1eb7c \u2264, v\u00ed d\u1ee5 2x + 1 &gt; 5.<\/p>\n<h3>Nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 g\u00ec?<\/h3>\n<p>L\u00e0 gi\u00e1 tr\u1ecb c\u1ee7a \u1ea9n l\u00e0m cho b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh tr\u1edf th\u00e0nh m\u1ec7nh \u0111\u1ec1 \u0111\u00fang; t\u1ea5t c\u1ea3 nghi\u1ec7m t\u1ea1o th\u00e0nh t\u1eadp nghi\u1ec7m.<\/p>\n<h3>Khi n\u00e0o ph\u1ea3i \u0111\u1ed5i chi\u1ec1u b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh?<\/h3>\n<p>Khi nh\u00e2n ho\u1eb7c chia c\u1ea3 hai v\u1ebf v\u1edbi m\u1ed9t s\u1ed1 \u00e2m th\u00ec ph\u1ea3i \u0111\u1ed5i chi\u1ec1u b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh.<\/p>\n<h3>B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh kh\u00e1c ph\u01b0\u01a1ng tr\u00ecnh th\u1ebf n\u00e0o?<\/h3>\n<p>Ph\u01b0\u01a1ng tr\u00ecnh d\u00f9ng d\u1ea5u b\u1eb1ng, c\u00f2n b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh d\u00f9ng d\u1ea5u b\u1ea5t \u0111\u1eb3ng th\u1ee9c v\u00e0 th\u01b0\u1eddng c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m t\u1ea1o th\u00e0nh m\u1ed9t kho\u1ea3ng.<\/p>\n<h3>Gi\u1ea3i 2x + 1 &gt; 5 cho k\u1ebft qu\u1ea3 g\u00ec?<\/h3>\n<p>x &gt; 2.<\/p>\n<h3>C\u00e1ch gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai nh\u01b0 th\u1ebf n\u00e0o?<\/h3>\n<p>\u0110\u01b0a v\u1ec1 d\u1ea1ng f(x) = ax\u00b2 + bx + c so v\u1edbi 0, t\u00ednh \u0394 \u0111\u1ec3 t\u00ecm nghi\u1ec7m (n\u1ebfu c\u00f3), r\u1ed3i d\u1ef1a v\u00e0o d\u1ea5u h\u1ec7 s\u1ed1 a v\u00e0 \u0111\u1ecbnh l\u00fd d\u1ea5u tam th\u1ee9c b\u1eadc hai \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh kho\u1ea3ng th\u1ecfa m\u00e3n.<\/p>\n<h3>B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a \u1ea9n \u1edf m\u1eabu c\u1ea7n l\u01b0u \u00fd g\u00ec?<\/h3>\n<p>Quy \u0111\u1ed3ng, \u0111\u01b0a v\u1ec1 d\u1ea1ng so v\u1edbi 0 r\u1ed3i l\u1eadp b\u1ea3ng x\u00e9t d\u1ea5u t\u1eed v\u00e0 m\u1eabu; gi\u00e1 tr\u1ecb l\u00e0m m\u1eabu s\u1ed1 b\u1eb1ng 0 ph\u1ea3i lo\u1ea1i kh\u1ecfi t\u1eadp nghi\u1ec7m, k\u1ec3 c\u1ea3 khi b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 d\u1ea5u \u2265 ho\u1eb7c \u2264.<\/p>\n<h3>H\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 g\u00ec?<\/h3>\n<p>L\u00e0 hai hay nhi\u1ec1u b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh c\u00f9ng m\u1ed9t \u1ea9n \u0111\u01b0\u1ee3c x\u00e9t \u0111\u1ed3ng th\u1eddi; t\u1eadp nghi\u1ec7m c\u1ee7a h\u1ec7 l\u00e0 giao (\u2229) t\u1eadp nghi\u1ec7m c\u1ee7a t\u1eebng b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh th\u00e0nh ph\u1ea7n.<\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>T\u00f3m l\u1ea1i, b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 m\u1ec7nh \u0111\u1ec1 ch\u1ee9a \u1ea9n n\u1ed1i b\u1eb1ng d\u1ea5u b\u1ea5t \u0111\u1eb3ng th\u1ee9c, gi\u1ea3i n\u00f3 l\u00e0 t\u00ecm t\u1eadp nghi\u1ec7m. Quy t\u1eafc quan tr\u1ecdng nh\u1ea5t l\u00e0 \u0111\u1ed5i chi\u1ec1u khi nh\u00e2n ho\u1eb7c chia hai v\u1ebf v\u1edbi s\u1ed1 \u00e2m, d\u00f9 l\u00e0 b\u1eadc nh\u1ea5t, b\u1eadc hai hay ch\u1ee9a \u1ea9n \u1edf m\u1eabu. N\u1eafm v\u1eefng quy t\u1eafc bi\u1ebfn \u0111\u1ed5i v\u00e0 b\u1ea3ng x\u00e9t d\u1ea5u, b\u1ea1n s\u1ebd gi\u1ea3i nhanh m\u1ecdi d\u1ea1ng b\u00e0i. Tham kh\u1ea3o th\u00eam c\u00e1c b\u00e0i <strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/tap-hop-so-nguyen-z-la-gi-giai-ma-toan-dien-ve-z-trong-toan-hoc\/\">t\u1eadp h\u1ee3p s\u1ed1 nguy\u00ean Z<\/a>, <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-to-hop-chinh-hop\/\">c\u00f4ng th\u1ee9c ho\u00e1n v\u1ecb, ch\u1ec9nh h\u1ee3p, t\u1ed5 h\u1ee3p<\/a><\/strong> v\u00e0 <strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-tam-giac\/\">di\u1ec7n t\u00edch tam gi\u00e1c<\/a><\/strong> tr\u00ean chuy\u00ean m\u1ee5c tin t\u1ee9c c\u1ee7a Ho\u00e0ng H\u00e0 Mobile.<br \/>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [\n    {\n      \"@type\": \"Question\",\n      \"name\": \"B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"L\u00e0 m\u1ec7nh \u0111\u1ec1 ch\u1ee9a \u1ea9n n\u1ed1i hai v\u1ebf b\u1eb1ng d\u1ea5u >, <, \u2265 ho\u1eb7c \u2264, v\u00ed d\u1ee5 2x + 1 > 5.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"Nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"L\u00e0 gi\u00e1 tr\u1ecb c\u1ee7a \u1ea9n l\u00e0m cho b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh tr\u1edf th\u00e0nh m\u1ec7nh \u0111\u1ec1 \u0111\u00fang; t\u1ea5t c\u1ea3 nghi\u1ec7m t\u1ea1o th\u00e0nh t\u1eadp nghi\u1ec7m.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"Khi n\u00e0o ph\u1ea3i \u0111\u1ed5i chi\u1ec1u b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Khi nh\u00e2n ho\u1eb7c chia c\u1ea3 hai v\u1ebf v\u1edbi m\u1ed9t s\u1ed1 \u00e2m th\u00ec ph\u1ea3i \u0111\u1ed5i chi\u1ec1u b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh kh\u00e1c ph\u01b0\u01a1ng tr\u00ecnh th\u1ebf n\u00e0o?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Ph\u01b0\u01a1ng tr\u00ecnh d\u00f9ng d\u1ea5u b\u1eb1ng, c\u00f2n b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh d\u00f9ng d\u1ea5u b\u1ea5t \u0111\u1eb3ng th\u1ee9c v\u00e0 th\u01b0\u1eddng c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m t\u1ea1o th\u00e0nh m\u1ed9t kho\u1ea3ng.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"Gi\u1ea3i 2x + 1 > 5 cho k\u1ebft qu\u1ea3 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"x > 2.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"C\u00e1ch gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai nh\u01b0 th\u1ebf n\u00e0o?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"\u0110\u01b0a v\u1ec1 d\u1ea1ng f(x) = ax\u00b2 + bx + c so v\u1edbi 0, t\u00ednh \u0394 \u0111\u1ec3 t\u00ecm nghi\u1ec7m (n\u1ebfu c\u00f3), r\u1ed3i d\u1ef1a v\u00e0o d\u1ea5u h\u1ec7 s\u1ed1 a v\u00e0 \u0111\u1ecbnh l\u00fd d\u1ea5u tam th\u1ee9c b\u1eadc hai \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh kho\u1ea3ng th\u1ecfa m\u00e3n.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a \u1ea9n \u1edf m\u1eabu c\u1ea7n l\u01b0u \u00fd g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Quy \u0111\u1ed3ng, \u0111\u01b0a v\u1ec1 d\u1ea1ng so v\u1edbi 0 r\u1ed3i l\u1eadp b\u1ea3ng x\u00e9t d\u1ea5u t\u1eed v\u00e0 m\u1eabu; gi\u00e1 tr\u1ecb l\u00e0m m\u1eabu s\u1ed1 b\u1eb1ng 0 ph\u1ea3i lo\u1ea1i kh\u1ecfi t\u1eadp nghi\u1ec7m, k\u1ec3 c\u1ea3 khi b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 d\u1ea5u \u2265 ho\u1eb7c \u2264.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"H\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"L\u00e0 hai hay nhi\u1ec1u b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh c\u00f9ng m\u1ed9t \u1ea9n \u0111\u01b0\u1ee3c x\u00e9t \u0111\u1ed3ng th\u1eddi; t\u1eadp nghi\u1ec7m c\u1ee7a h\u1ec7 l\u00e0 giao (\u2229) t\u1eadp nghi\u1ec7m c\u1ee7a t\u1eebng b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh th\u00e0nh ph\u1ea7n.\"\n      }\n    }\n  ]\n}\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 ch\u1ee9a \u1ea9n, trong \u0111\u00f3 hai v\u1ebf \u0111\u01b0\u1ee3c n\u1ed1i v\u1edbi nhau b\u1eb1ng m\u1ed9t trong c\u00e1c d\u1ea5u b\u1ea5t \u0111\u1eb3ng th\u1ee9c: l\u1edbn h\u01a1n (&gt;), nh\u1ecf h\u01a1n (&lt;), l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng (\u2265), nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng (\u2264). V\u00ed d\u1ee5 2x + 1 &gt; 5 l\u00e0 m\u1ed9t b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh. Gi\u1ea3i b\u1ea5t [&hellip;]<\/p>\n","protected":false},"author":65,"featured_media":567754,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh","_yoast_wpseo_title":"B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 g\u00ec? C\u00e1ch gi\u1ea3i, v\u00ed d\u1ee5","_yoast_wpseo_metadesc":"B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 g\u00ec, quy t\u1eafc bi\u1ebfn \u0111\u1ed5i v\u00e0 c\u00e1ch gi\u1ea3i b\u1eadc nh\u1ea5t, b\u1eadc hai, ch\u1ee9a \u1ea9n \u1edf m\u1eabu k\u00e8m v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, d\u1ec5 hi\u1ec3u t\u1eebng b\u01b0\u1edbc cho h\u1ecdc sinh.","footnotes":""},"categories":[16],"tags":[],"class_list":["post-567228","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-thu-thuat"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 g\u00ec? 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