Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
Trong to\u00e1n h\u1ecdc, ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 ch\u1ee9a t\u00edch l\u00e0 ki\u1ebfn th\u1ee9c r\u1ea5t quan tr\u1ecdng m\u00e0 b\u1ea5t c\u1ee9 h\u1ecdc sinh<\/a> n\u00e0o c\u0169ng ph\u1ea3i bi\u1ebft. Do \u0111\u00f3, th\u00f4ng qua b\u00e0i vi\u1ebft sau \u0111\u00e2y, Vietlearn s\u1ebd gi\u1edbi thi\u1ec7u \u0111\u1ebfn c\u00e1c b\u1ea1n \u0111\u1ecdc kh\u00e1i ni\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh t\u00edch c\u00f9ng v\u1edbi c\u00e1ch gi\u1ea3i \u0111\u1ed1i v\u1edbi lo\u1ea1i ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y.<\/p>\n\n\n\n Kh\u00e1i ni\u1ec7m v\u1ec1 ph\u01b0\u01a1ng tr\u00ecnh t\u00edch<\/p>\n\n\n\n Ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 ch\u1ee9a t\u00edch bao g\u1ed3m 2 v\u1ebf, 1 v\u1ebf l\u00e0 t\u00edch c\u1ee7a c\u00e1c \u0111a th\u1ee9c, v\u1ebf c\u00f2n l\u1ea1i s\u1ebd b\u1eb1ng 0. Ph\u01b0\u01a1ng tr\u00ecnh t\u00edch \u0111\u01b0\u1ee3c vi\u1ebft d\u01b0\u1edbi d\u1ea1ng t\u1ed5ng qu\u00e1t l\u00e0 f1(x)f2(x)f3(x)\u2026fn(x) = 0.<\/p>\n\n\n\n Trong \u0111\u00f3, fi(x) l\u00e0 nh\u1eefng h\u00e0m s\u1ed1 c\u00f3 ch\u1ee9a \u1ea9n x. H\u1ee3p c\u1ee7a c\u00e1c t\u1eadp nghi\u1ec7m c\u1ee7a nh\u1eefng ph\u01b0\u01a1ng tr\u00ecnh fi(x) v\u1edbi x= 1,2\u2026 c\u0169ng s\u1ebd l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 ch\u1ee9a t\u00edch \u0111\u00f3.<\/p>\n\n\n\n Ph\u01b0\u01a1ng tr\u00ecnh t\u00edch l\u1edbp 8 l\u00e0 nh\u1eefng ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n<\/a> m\u00e0 h\u1ecdc sinh<\/a> c\u1ea7n ph\u1ea3i n\u1eafm \u0111\u01b0\u1ee3c \u0111\u1ec3 gi\u1ea3i nhi\u1ec1u b\u00e0i t\u1eadp ph\u1ee9c t\u1ea1p kh\u00e1c. Do \u0111\u00f3, vi\u1ec7c t\u00ecm hi\u1ec3u c\u00e1ch gi\u1ea3i \u0111\u1ed1i v\u1edbi to\u00e1n 8 ph\u01b0\u01a1ng tr\u00ecnh t\u00edch l\u00e0 v\u00f4 c\u00f9ng quan tr\u1ecdng.<\/p>\n\n\n\n Ph\u01b0\u01a1ng tr\u00ecnh t\u00edch l\u00e0 g\u00ec?<\/p>\n\n\n\n Quy tr\u00ecnh gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh t\u00edch<\/p>\n\n\n\n \u0110\u1ec3 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh t\u00edch, c\u00e1c b\u1ea1n c\u1ea7n ph\u1ea3i th\u1ef1c hi\u1ec7n theo 2 b\u01b0\u1edbc c\u01a1 b\u1ea3n.<\/p>\n\n\n\n B\u01b0\u1edbc 1<\/p>\n\n\n\n B\u01b0\u1edbc \u0111\u1ea7u ti\u00ean trong c\u00e1ch gi\u1ea3i l\u00e0 ph\u1ea3i \u0111\u01b0a ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1ee3c cho trong \u0111\u1ec1 b\u00e0i v\u1ec1 d\u01b0\u1edbi d\u1ea1ng t\u1ed5ng qu\u00e1t.<\/p>\n\n\n\n D\u1ea1ng t\u1ed5ng qu\u00e1t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 ch\u1ee9a t\u00edch l\u00e0 d\u1ea1ng A(x).B(x) = 0, \u0111\u01b0\u1ee3c \u0111\u01b0a v\u1ec1 b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p sau \u0111\u00e2y:<\/p>\n\n\n\n Chuy\u1ec3n t\u1ea5t c\u1ea3 nh\u1eefng h\u1ea1ng t\u1eed t\u1eeb v\u1ebf ph\u1ea3i sang v\u1ebf tr\u00e1i, v\u1ebf ph\u1ea3i s\u1ebd b\u1eb1ng kh\u00f4ng.<\/p>\n\n\n\n S\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed \u0111\u1ec3 ph\u00e2n t\u00edch v\u1ebf tr\u00e1i th\u00e0nh c\u00e1c nh\u00e2n t\u1eed.<\/p>\n\n\n\n B\u01b0\u1edbc 2<\/p>\n\n\n\n \u0110\u00e2y l\u00e0 b\u01b0\u1edbc t\u00ecm nghi\u1ec7m cho lo\u1ea1i ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y. Ph\u01b0\u01a1ng ph\u00e1p t\u00ecm nghi\u1ec7m s\u1ebd t\u00f9y thu\u1ed9c v\u00e0o \u0111\u01a1n th\u1ee9c. \u0110\u1ec3 t\u00ecm nghi\u1ec7m, b\u1ea1n ho\u00e0n to\u00e0n c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng nhi\u1ec1u ph\u01b0\u01a1ng ph\u00e1p kh\u00e1c nhau.<\/p>\n\n\n\n Khi A(x).B(x) = 0 th\u00ec A(x) = 0 ho\u1eb7c B (x) = 0.<\/p>\n\n\n\n 2 b\u01b0\u1edbc \u0111\u1ec3 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh<\/p>\n\n\n\n Gi\u1ea3i b\u00e0i to\u00e1n b\u1eb1ng c\u00e1ch l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh<\/p><\/blockquote>\n\n\n\n C\u00e1ch gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh t\u00edch<\/p>\n\n\n\n Nh\u01b0 Vietlearn \u0111\u00e3 \u0111\u1ec1 c\u1eadp \u1edf ph\u1ea7n b\u00ean tr\u00ean, ph\u01b0\u01a1ng tr\u00ecnh t\u00edch c\u00f3 nhi\u1ec1u ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i kh\u00e1c nhau, t\u00f9y thu\u1ed9c v\u00e0o c\u00e1c \u0111\u01a1n th\u1ee9c m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 l\u1ef1a ch\u1ecdn c\u00e1ch gi\u1ea3i ph\u00f9 h\u1ee3p. Tr\u01b0\u1edbc ti\u00ean, c\u1ea7n ph\u1ea3i \u0111\u01b0a nh\u00e2n t\u1eed v\u1ec1 v\u1ebf tr\u00e1i, b\u1ea1n c\u1ea7n n\u1eafm r\u00f5 nh\u1eefng ph\u01b0\u01a1ng ph\u00e1p ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed \u0111\u1ec3 c\u00f3 th\u1ec3 l\u00e0m t\u1ed1t b\u01b0\u1edbc n\u00e0y.<\/p>\n\n\n\n Ph\u01b0\u01a1ng ph\u00e1p \u0111\u1eb7t nh\u00e2n t\u1eed chung<\/p>\n\n\n\n Ph\u01b0\u01a1ng ph\u00e1p \u0111\u1eb7t nh\u00e2n t\u1eed chung l\u00e0 ph\u01b0\u01a1ng ph\u00e1p c\u01a1 b\u1ea3n nh\u1ea5t khi ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed. B\u1ea1n c\u1ea7n ph\u1ea3i th\u1ef1c hi\u1ec7n 3 b\u01b0\u1edbc \u0111\u1ec3 ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed:<\/p>\n\n\n\n B\u01b0\u1edbc 1: Bi\u1ebfn \u0111\u1ed5i \u0111a th\u1ee9c A(x) theo d\u1ea1ng A(x) = C(x).A1(x), bi\u1ebfn \u0111\u1ed5i \u0111a th\u1ee9c B(x) theo d\u1ea1ng B(x) = C(x).B1(x).<\/p>\n\n\n\n B\u01b0\u1edbc 2: Sau khi bi\u1ebfn \u0111\u1ed5i c\u00e1c \u0111a th\u1ee9c, ph\u01b0\u01a1ng tr\u00ecnh s\u1ebd c\u00f3 d\u1ea1ng A(x)+B(x) = C(x).[A1(x)+B1(x)].<\/p>\n\n\n\n B\u01b0\u1edbc 3: Gi\u1ea3i l\u1ea7n l\u01b0\u1ee3t t\u1eebng ph\u01b0\u01a1ng tr\u00ecnh ri\u00eang l\u1ebb C(x) = 0 v\u00e0 A1(x)+B1(x) = 0.<\/p>\n\n\n\n Ph\u01b0\u01a1ng ph\u00e1p h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb<\/p>\n\n\n\n C\u00e1c h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb l\u00e0 nh\u1eefng ki\u1ebfn th\u1ee9c v\u00f4 c\u00f9ng quen thu\u1ed9c v\u00e0 quan tr\u1ecdng trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n<\/a> h\u1ecdc, \u0111\u00e2y c\u0169ng l\u00e0 ph\u01b0\u01a1ng ph\u00e1p th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng khi ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed. Sau \u0111\u00e2y l\u00e0 c\u00e1c h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb c\u01a1 b\u1ea3n m\u00e0 h\u1ecdc sinh<\/a> c\u1ea7n ph\u1ea3i n\u1eafm r\u00f5.<\/p>\n\n\n\n 7 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb<\/p>\n\n\n\n B\u00ean c\u1ea1nh 7 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb c\u01a1 b\u1ea3n tr\u00ean, c\u00e1c b\u1ea1n c\u00f2n c\u1ea7n ph\u1ea3i l\u01b0u \u00fd nh\u1eefng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c sau:<\/p>\n\n\n\n a4 \u2013 b4 = (a2 + b2).(a \u2013 b).(a + b)<\/p>\n\n\n\n (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac<\/p>\n\n\n\n (a + b + c)3 = a3 + b3 + c3 + 3.(a + b).(b + c).(c + a)<\/p>\n\n\n\n (a + b).(b + c).(c + a) = (a + b+ c).(ab + bc + ca) \u2013 abc<\/p>\n\n\n\n Ph\u01b0\u01a1ng ph\u00e1p t\u00e1ch \u0111\u1ec3 xu\u1ea5t hi\u1ec7n nh\u00e2n t\u1eed chung<\/p>\n\n\n\n \u0110\u1ec3 s\u1eed d\u1ee5ng t\u1ed1t ph\u01b0\u01a1ng ph\u00e1p t\u00e1ch, c\u00e1c b\u1ea1n c\u1ea7n ph\u1ea3i n\u1eafm \u0111\u01b0\u1ee3c \u0111\u1ecbnh l\u00fd quan tr\u1ecdng sau \u0111\u00e2y:<\/p>\n\n\n\n Khi m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh f(x) = 0 c\u00f3 nghi\u1ec7m l\u00e0 x = a th\u00ec f(x) c\u00f2n c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c vi\u1ebft d\u01b0\u1edbi d\u1ea1ng l\u00e0 f(x) = (x \u2013 a).g(x).<\/p>\n\n\n\n Do \u0111\u00f3, khi b\u1ea1n nh\u1ea9m \u0111\u01b0\u1ee3c nghi\u1ec7m nguy\u00ean c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh t\u00edch th\u00ec b\u1ea1n ho\u00e0n to\u00e0n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p t\u00e1ch \u0111\u1ec3 l\u00e0m xu\u1ea5t hi\u1ec7n nh\u00e2n t\u1eed (x \u2013 a).<\/p>\n\n\n\n V\u1edbi b\u00e0i to\u00e1n c\u00f3 d\u1ea1ng A(x) + B(x) + C(x) = 0, ch\u00fang ta c\u00f3 th\u1ec3 th\u1ef1c hi\u1ec7n theo c\u00e1ch sau:<\/p>\n\n\n\n T\u00e1ch C(x) = C1(x) + C2(x) \u0111\u1ec3 A(x) + C1(x) v\u00e0 B(x) + C2(x) c\u00f3 xu\u1ea5t hi\u1ec7n nh\u00e2n t\u1eed chung.<\/p>\n\n\n\n Ph\u01b0\u01a1ng ph\u00e1p th\u00eam b\u1edbt \u0111\u1ec3 xu\u1ea5t hi\u1ec7n nh\u00e2n t\u1eed chung<\/p>\n\n\n\n T\u01b0\u01a1ng t\u1ef1 nh\u01b0 ph\u01b0\u01a1ng ph\u00e1p t\u00e1ch, \u0111\u1ed1i v\u1edbi ph\u01b0\u01a1ng ph\u00e1p th\u00eam b\u1edbt, ch\u00fang ta c\u00f3 th\u1ec3 nh\u1ea9m tr\u01b0\u1edbc nghi\u1ec7m nguy\u00ean a v\u00e0 sau \u0111\u00f3 t\u00ecm c\u00e1ch \u0111\u1ec3 xu\u1ea5t hi\u1ec7n nh\u00e2n t\u1eed chung (x \u2013 a).<\/p>\n\n\n\n V\u1edbi b\u00e0i to\u00e1n A(x) + B (x) = 0, c\u00e1c b\u1ea1n th\u00eam \u0111\u1ea1i l\u01b0\u1ee3ng C(x) v\u00e0o A(x) v\u00e0 b\u1edbt \u0111i \u0111\u1ea1i l\u01b0\u1ee3ng C(x) \u1edf B(x) sao cho 2 t\u1ed5ng A(x) + C(x) v\u00e0 B(x) \u2013 C(x) c\u00f3 xu\u1ea5t hi\u1ec7n nh\u00e2n t\u1eed chung.<\/p>\n\n\n\n \u0110i\u1ec1u quan tr\u1ecdng m\u00e0 c\u00e1c b\u1ea1n c\u1ea7n l\u01b0u \u00fd l\u00e0 c\u1ea7n ph\u1ea3i nh\u1ea9m \u0111\u01b0\u1ee3c tr\u01b0\u1edbc nghi\u1ec7m nguy\u00ean c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh t\u00edch, sau \u0111\u00f3 s\u1ebd t\u00ecm \u0111\u01b0\u1ee3c ph\u01b0\u01a1ng ph\u00e1p t\u00e1ch ho\u1eb7c ph\u01b0\u01a1ng ph\u00e1p th\u00eam b\u1edbt h\u1ee3p l\u00fd \u0111\u1ec3 l\u00e0m xu\u1ea5t hi\u1ec7n nh\u00e2n t\u1eed chung, sau \u0111\u00f3 ti\u1ebfn h\u00e0nh gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a t\u00edch theo \u0111\u00fang quy tr\u00ecnh.<\/p>\n\n\n\n B\u00e0i vi\u1ebft tr\u00ean c\u1ee7a Vietlearn \u0111\u00e3 ph\u00e2n t\u00edch chi ti\u1ebft nh\u1eefng ki\u1ebfn th\u1ee9c li\u00ean quan \u0111\u1ebfn ph\u01b0\u01a1ng tr\u00ecnh t\u00edch c\u0169ng nh\u01b0 c\u00e1ch gi\u1ea3i \u0111\u1ed1i v\u1edbi lo\u1ea1i b\u00e0i t\u1eadp n\u00e0y. \u0110\u1ec3 t\u00ecm hi\u1ec3u th\u00eam v\u1ec1 c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh To\u00e1n h\u1ecdc kh\u00e1c, h\u00e3y truy c\u1eadp ngay v\u00e0o trang web Vietlearn.org\/ c\u00e1c b\u1ea1n nh\u00e9.<\/p>\n\n\n\n T\u00ecm hi\u1ec3u th\u00eam:<\/p>\n\n\n\n Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t m\u1ed9t \u1ea9n v\u00e0 c\u00e1ch gi\u1ea3i<\/p>\n\n\n\n Ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed b\u1eb1ng 8 ph\u01b0\u01a1ng ph\u00e1p \u2013 To\u00e1n h\u1ecdc 8<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":" Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn Trong to\u00e1n h\u1ecdc, ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 ch\u1ee9a t\u00edch l\u00e0 ki\u1ebfn th\u1ee9c r\u1ea5t quan tr\u1ecdng m\u00e0 b\u1ea5t c\u1ee9 h\u1ecdc sinh n\u00e0o c\u0169ng ph\u1ea3i bi\u1ebft. Do \u0111\u00f3, th\u00f4ng qua b\u00e0i vi\u1ebft sau \u0111\u00e2y, Vietlearn s\u1ebd gi\u1edbi thi\u1ec7u \u0111\u1ebfn c\u00e1c b\u1ea1n \u0111\u1ecdc kh\u00e1i ni\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh t\u00edch c\u00f9ng v\u1edbi c\u00e1ch gi\u1ea3i \u0111\u1ed1i […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[9],"tags":[],"class_list":["post-921","post","type-post","status-publish","format-standard","hentry","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/921","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=921"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/921\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=921"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=921"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=921"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}