{"id":303551,"date":"2024-01-06T15:15:59","date_gmt":"2024-01-06T08:15:59","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=303551"},"modified":"2024-01-06T15:15:59","modified_gmt":"2024-01-06T08:15:59","slug":"so-huu-ti-la-gi","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/so-huu-ti-la-gi\/","title":{"rendered":"S\u1ed1 h\u1eefu t\u1ec9 l\u00e0 g\u00ec? S\u1ed1 v\u00f4 t\u1ec9 l\u00e0 g\u00ec? \u0110\u1eb7c tr\u01b0ng c\u1ee7a c\u00e1c s\u1ed1 trong To\u00e1n h\u1ecdc"},"content":{"rendered":"

To\u00e1n h\u1ecdc cung c\u1ea5p cho c\u00e1c l\u1ee9a h\u1ecdc sinh, sinh vi\u00ean nh\u1eefng ki\u1ebfn th\u1ee9c quan tr\u1ecdng \u0111\u1ec3 l\u00e0m c\u01a1 s\u1edf \u1ee9ng d\u1ee5ng v\u00e0o th\u1ef1c ti\u1ec5n. Trong \u0111\u00f3 c\u00e1c lo\u1ea1i s\u1ed1 c\u01a1 b\u1ea3n l\u00e0 m\u1ed9t trong nh\u1eefng l\u00fd thuy\u1ebft \u0111i\u1ec3n h\u00ecnh m\u00e0 b\u1ea5t c\u1ee9 ng\u01b0\u1eddi h\u1ecdc n\u00e0o c\u0169ng c\u1ea7n n\u1eafm \u0111\u01b0\u1ee3c. Ngo\u00e0i s\u1ed1 t\u1ef1 nhi\u00ean, s\u1ed1 nguy\u00ean \u0111\u01a1n gi\u1ea3n, ng\u01b0\u1eddi h\u1ecdc s\u1ebd \u0111\u01b0\u1ee3c ti\u1ebfp x\u00fac v\u1edbi kh\u00e1i ni\u1ec7m s\u1ed1 h\u1eefu t\u1ec9 v\u00e0 s\u1ed1 v\u00f4 t\u1ec9. T\u1eadp h\u1ee3p c\u00e1c s\u1ed1 n\u00e0y v\u00f4 c\u00f9ng r\u1ed9ng l\u1edbn v\u00e0 \u0111\u01b0\u1ee3c b\u1eaft g\u1eb7p r\u1ea5t nhi\u1ec1u t\u1eeb trong s\u00e1ch \u0111\u1ec3 \u0111\u1eddi th\u1ef1c. V\u1eady th\u1ef1c ch\u1ea5t <\/span>s\u1ed1 h\u1eefu t\u1ec9 l\u00e0 g\u00ec<\/b> v\u00e0<\/span> s\u1ed1 v\u00f4 t\u1ec9 l\u00e0 g\u00ec<\/b>? \u0110\u1eb7c \u0111i\u1ec3m v\u00e0 s\u1ef1 kh\u00e1c nhau c\u1ee7a hai lo\u1ea1i s\u1ed1 n\u00e0y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ph\u00e2n bi\u1ec7t theo c\u00e1ch n\u00e0o? H\u00e3y c\u00f9ng <\/span>Ho\u00e0ng H\u00e0 Mobile<\/b> kh\u00e1m ph\u00e1 v\u1ec1 nh\u1eefng ki\u1ebfn th\u1ee9c To\u00e1n h\u1ecdc b\u1ed5 \u00edch trong b\u00e0i vi\u1ebft ng\u00e0y h\u00f4m nay nh\u00e9!<\/span><\/p>\n

T\u1ed5ng quan chung v\u1ec1 s\u1ed1 h\u1eefu t\u1ec9 trong To\u00e1n h\u1ecdc<\/b><\/h2>\n

Theo ch\u01b0\u01a1ng tr\u00ecnh \u0111\u00e0o t\u1ea1o hi\u1ec7n nay, h\u1ecdc sinh s\u1ebd \u0111\u01b0\u1ee3c l\u00e0m quen v\u1edbi s\u1ed1 h\u1eefu t\u1ec9 t\u1eeb To\u00e1n c\u1ea5p Ti\u1ec3u h\u1ecdc, sau \u0111\u00f3 h\u1ecdc s\u00e2u h\u01a1n v\u1ec1 c\u00e1c ph\u00e9p t\u00ednh v\u00e0 c\u00f4ng th\u1ee9c li\u00ean quan \u0111\u1ebfn lo\u1ea1i s\u1ed1 n\u00e0y v\u00e0o c\u1ea5p THCS v\u00e0 THPT. S\u1ed1 h\u1eefu t\u1ec9 l\u00e0 m\u1ed9t ki\u1ebfn th\u1ee9c r\u1ea5t quan tr\u1ecdng, l\u00e0 n\u1ec1n t\u1ea3ng \u0111\u1ec3 ph\u00e1t tri\u1ec3n t\u01b0 duy c\u00e1c b\u00e0i t\u1eadp cao c\u1ea5p h\u01a1n v\u1ec1 sau n\u00e0y. Ph\u1ea7n \u0111\u1ea7u c\u1ee7a b\u00e0i vi\u1ebft s\u1ebd mang \u0111\u1ebfn nh\u1eefng th\u00f4ng tin c\u0103n b\u1ea3n nh\u1ea5t v\u1ec1 s\u1ed1 h\u1eefu t\u1ec9 cho ng\u01b0\u1eddi \u0111\u1ecdc.<\/span><\/p>\n

S\u1ed1 h\u1eefu t\u1ec9 l\u00e0 g\u00ec? Kh\u00e1i ni\u1ec7m s\u1ed1 h\u1eefu t\u1ec9<\/b><\/h3>\n

S\u1ed1 h\u1eefu t\u1ec9 l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 c\u00f3 th\u1ec3 vi\u1ebft \u0111\u01b0\u1ee3c d\u01b0\u1edbi ph\u00e2n s\u1ed1 c\u00f3 d\u1ea1ng a\/b. Trong \u0111\u00f3, c\u1ea3 a v\u00e0 b ph\u1ea3i l\u00e0 s\u1ed1 nguy\u00ean (bao g\u1ed3m c\u1ea3 s\u1ed1 \u00e2m v\u00e0 s\u1ed1 d\u01b0\u01a1ng), b ph\u1ea3i kh\u00e1c 0. Quy \u0111\u1ecbnh v\u1ec1 d\u1ea1ng ph\u00e2n s\u1ed1 c\u1ee7a s\u1ed1 h\u1eefu t\u1ec9 ho\u00e0n to\u00e0n tu\u00e2n theo quy \u01b0\u1edbc kh\u00f4ng c\u00f3 s\u1ed1 n\u00e0o c\u00f3 th\u1ec3 chia \u0111\u01b0\u1ee3c cho 0. V\u00ec v\u1eady, trong tr\u01b0\u1eddng h\u1ee3p b = 0, s\u1ed1 h\u1eefu t\u1ec9 \u0111\u00f3 s\u1ebd l\u00e0 s\u1ed1 v\u00f4 ngh\u0129a. \u0110\u00e2y c\u0169ng l\u00e0 \u0111\u1ecbnh ngh\u0129a c\u01a1 b\u1ea3n v\u00e0 d\u1ec5 hi\u1ec3u nh\u1ea5t c\u1ee7a s\u1ed1 h\u1eefu t\u1ec9, \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 gi\u1edbi thi\u1ec7u t\u1edbi ng\u01b0\u1eddi h\u1ecdc trong c\u00e1c ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n h\u1ecdc chu\u1ea9n s\u00e1ch gi\u00e1o khoa. Ng\u01b0\u1eddi h\u1ecdc s\u1ebd d\u1ec5 d\u00e0ng b\u1eaft g\u1eb7p s\u1ed1 h\u1eefu t\u1ec9 trong nhi\u1ec1u ph\u00e9p t\u00ednh to\u00e1n nh\u01b0 c\u1ed9ng tr\u1eeb nh\u00e2n chia, l\u0169y th\u1eeba, k\u1ebft qu\u1ea3 c\u1ee7a t\u00edch ph\u00e2n, nguy\u00ean ph\u00e2n\u2026<\/span><\/p>\n

\"so-huu-ti-la-gi-1\"<\/p>\n

Kh\u00e1i ni\u1ec7m s\u1ed1 h\u1eefu t\u1ec9 l\u00e0 g\u00ec kh\u00f4ng ch\u1ec9 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng cho To\u00e1n h\u1ecdc m\u00e0 c\u00f2n l\u00e0 c\u01a1 s\u1edf t\u00ednh to\u00e1n c\u1ee7a nhi\u1ec1u m\u00f4n h\u1ecdc t\u1ef1 nhi\u00ean kh\u00e1c V\u1eadt l\u00fd, H\u00f3a h\u1ecdc v\u00e0 Sinh h\u1ecdc. S\u1ed1 h\u1eefu t\u1ec9 gi\u00fap ng\u01b0\u1eddi h\u1ecdc th\u1ec3 hi\u1ec7n \u0111\u01b0\u1ee3c c\u00e1c s\u1ed1 kh\u00f4ng ph\u1ea3i d\u1ea1ng s\u1ed1 nguy\u00ean th\u00f4ng th\u01b0\u1eddng, ho\u1eb7c h\u00ecnh dung r\u00f5 h\u01a1n v\u1ec1 t\u1ef7 l\u1ec7, c\u00e1ch chia ph\u1ea7n\u2026 Lo\u1ea1i s\u1ed1 n\u00e0y \u0111\u01b0\u1ee3c ra \u0111\u1eddi c\u00f9ng v\u1edbi kh\u00e1i ni\u1ec7m ph\u00e2n s\u1ed1, c\u0169ng c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c vi\u1ebft d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n v\u1edbi d\u1ea5u ph\u1ea9y ng\u0103n c\u00e1ch gi\u1eefa ph\u1ea7n nguy\u00ean v\u00e0 ph\u1ea7n th\u1eadp ph\u00e2n. Tuy nhi\u00ean \u0111\u1ec3 d\u1ec5 h\u00ecnh dung, c\u00e1c k\u1ebft qu\u1ea3 c\u1ee7a s\u1ed1 h\u1eefu t\u1ec9 th\u01b0\u1eddng \u0111\u01b0\u1ee3c bi\u1ec3u hi\u1ec7n d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1 a\/b (a, b thu\u1ed9c <\/span>\ud835\udd6b<\/span> v\u00e0 b kh\u00e1c <\/span>0).<\/span><\/p>\n

Gi\u1edbi thi\u1ec7u v\u1ec1 t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 h\u1eefu t\u1ec9<\/b><\/h3>\n

T\u1eadp h\u1ee3p c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 \u211a v\u1edbi ki\u1ec3u ch\u1eef vi\u1ec1n ho\u1eb7c ch\u1eef <\/span>Q<\/b> in \u0111\u1eadm, vi\u1ebft t\u1eaft c\u1ee7a t\u1eeb quoziente c\u00f3 ngh\u0129a l\u00e0 t\u1ef7 l\u1ec7. Theo \u0111\u00fang nguy\u00ean t\u1eafc, t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 s\u1ebd l\u00e0 t\u1eadp h\u1ee3p con t\u1eadp s\u1ed1 th\u1ef1c \u211d, t\u1ee9c l\u00e0 t\u1eadp s\u1ed1 th\u1ef1c r\u1ed9ng h\u01a1n v\u00e0 bao g\u1ed3m t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 h\u1eefu t\u1ec9. Ngo\u00e0i ra, t\u1eadp h\u1ee3p \u211a l\u1ea1i bao h\u00e0m c\u00e1c t\u1eadp h\u1ee3p s\u1ed1 t\u1ef1 nhi\u00ean \u2115 v\u00e0 s\u1ed1 nguy\u00ean \u2124. M\u1ed9t v\u00e0i t\u00ednh ch\u1ea5t m\u00e0 ng\u01b0\u1eddi h\u1ecdc c\u1ea7n ghi nh\u1edb v\u1ec1 t\u1eadp h\u1ee3p s\u1ed1 h\u1eefu t\u1ec9 c\u00f2n bao g\u1ed3m <\/span>Q<\/b> l\u00e0 t\u1eadp h\u1ee3p s\u1ed1 \u0111\u1ebfm \u0111\u01b0\u1ee3c, bao h\u00e0m c\u1ea3 s\u1ed1 nguy\u00ean, s\u1ed1 th\u1eadp ph\u00e2n h\u1eefu h\u1ea1n v\u00e0 s\u1ed1 th\u1eadp ph\u00e2n v\u00f4 h\u1ea1n tu\u1ea7n ho\u00e0n.<\/span><\/p>\n

\"so-huu-ti-la-gi-2\"<\/p>\n

Kh\u00e1i ni\u1ec7m t\u1eadp h\u1ee3p s\u1ed1 h\u1eefu t\u1ec9 l\u00e0 g\u00ec r\u1ea5t d\u1ec5 hi\u1ec3u, th\u01b0\u1eddng \u0111\u01b0\u1ee3c vi\u1ebft t\u1eaft trong To\u00e1n h\u1ecdc nh\u01b0 sau: <\/span>Q <\/b>= {a\/b; a, b thu\u1ed9c <\/span>\ud835\udd6b<\/span> ; b kh\u00e1c <\/span>0}. Ngo\u00e0i ra c\u00e1c ph\u1ea7n t\u1eed trong t\u1eadp h\u1ee3p n\u00e0y c\u0169ng c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n tr\u00ean m\u1ed9t tr\u1ee5c th\u1eb3ng n\u1eb1m ngang v\u1edbi c\u00e1c v\u1ea1ch chia kho\u1ea3ng v\u00e0 ghi r\u00f5 s\u1ed1. Ng\u01b0\u1eddi h\u1ecdc c\u1ea7n nh\u1edb k\u1ef9 c\u00e1c k\u00fd hi\u1ec7u t\u1eadp h\u1ee3p \u0111\u1ec3 tr\u00e1nh s\u1ef1 nh\u1ea7m l\u1eabn trong khi gi\u1ea3i b\u00e0i t\u1eadp ho\u1eb7c \u1ee9ng d\u1ee5ng th\u1ef1c ti\u1ec5n. B\u00ean c\u1ea1nh \u0111\u00f3, b\u1ea1n c\u0169ng c\u1ea7n hi\u1ec3u r\u00f5 b\u1ea3n ch\u1ea5t c\u1ee7a s\u1ed1 h\u1eefu t\u1ec9 \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh \u0111\u00fang c\u00e1c ph\u1ea7n t\u1eed trong t\u1eadp <\/span>Q<\/b>, h\u1ea1n ch\u1ebf tr\u01b0\u1eddng h\u1ee3p nh\u1ea7m l\u1eabn v\u1edbi s\u1ed1 v\u00f4 t\u1ec9 ho\u1eb7c s\u1ed1 \u1ea3o.<\/span><\/p>\n

Gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a m\u1ed9t s\u1ed1 h\u1eefu t\u1ec9 l\u00e0 g\u00ec?<\/b><\/h3>\n

C\u0169ng gi\u1ed1ng nh\u01b0 gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a c\u00e1c s\u1ed1 nguy\u00ean, tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a s\u1ed1 h\u1eefu t\u1ec9 l\u00e0 kho\u1ea3ng c\u00e1ch gi\u1eefa s\u1ed1 \u0111\u00f3 \u0111\u1ed1i v\u1edbi g\u1ed1c 0 tr\u00ean tr\u1ee5c t\u1ecda \u0111\u1ed9. N\u00f3i m\u1ed9t c\u00e1ch d\u1ec5 hi\u1ec3u, gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a m\u1ed9t s\u1ed1 h\u1eefu t\u1ec9 s\u1ebd l\u00e0 ph\u1ea7n d\u01b0\u01a1ng c\u1ee7a s\u1ed1 \u0111\u00f3, ngo\u1ea1i tr\u1eeb s\u1ed1 0 v\u00ec gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a 0 l\u00e0 ch\u00ednh n\u00f3. Kh\u00e1i ni\u1ec7m n\u00e0y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u nh\u01b0 sau: |x| v\u1edbi x <\/span> Q.<\/b><\/p>\n

\"so-huu-ti-la-gi-3\"<\/p>\n

Theo quy \u01b0\u1edbc, ng\u01b0\u1eddi h\u1ecdc s\u1ebd c\u00f3 k\u1ebft qu\u1ea3 gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a m\u1ed9t s\u1ed1 h\u1eefu t\u1ec9 x nh\u01b0 sau:<\/span><\/p>\n