Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
To\u00e1n 9 cung c\u1ea5p cho em h\u1ecdc sinh<\/a> c\u00e1c ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n<\/a> v\u00e0 n\u00e2ng cao v\u1ec1 ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh. Trong n\u1ed9i dung b\u00e0i h\u1ecdc h\u00f4m nay, Vietlearn s\u1ebd h\u01b0\u1edbng d\u1eabn c\u00e1c em gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf hi\u1ec7u qu\u1ea3 nh\u00e9. C\u00f9ng b\u1eaft tay v\u00e0o h\u1ecdc ngay th\u00f4i.<\/p>\n\n\n\n Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf<\/p>\n\n\n\n Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n v\u00e0 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<\/p>\n\n\n\n Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i h\u1ec7 pt b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf l\u00e0 m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p \u00e1p d\u1ee5ng cho h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n. Th\u1ebf n\u00ean, ch\u00fang ta c\u1ea7n hi\u1ec3u qua v\u1ec1 kh\u00e1i ni\u1ec7m chung c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n l\u00e0 th\u1ebf n\u00e0o \u0111\u00e3 nh\u00e9.<\/p>\n\n\n\n Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<\/p>\n\n\n\n Bi\u1ec3u th\u1ee9c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n \u0111\u01b0\u1ee3c vi\u1ebft nh\u01b0 sau: ax + by = c v\u1edbi a,b,c \u2282 R (a2+b2 # 0). Trong ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n, t\u1eadp nghi\u1ec7m c\u1ee7a n\u00f3 lu\u00f4n l\u00e0 c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m. T\u1eadp nghi\u1ec7m \u0111\u01b0\u1ee3c bi\u1ec3u th\u1ecb b\u1eb1ng \u0111\u01b0\u1eddng th\u1eb3ng (d): ax + by = c.<\/p>\n\n\n\n Ch\u00fang ta c\u0169ng c\u00f3 3 tr\u01b0\u1eddng h\u1ee3p sau:<\/p>\n\n\n\n N\u1ebfu a # 0 v\u00e0 b # 0: \u0111\u01b0\u1eddng th\u1eb3ng d c\u00f3 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 l\u00e0 y = \u2013 a\/b + c\/b<\/p>\n\n\n\n N\u1ebfu a # 0 v\u00e0 b = 0, ph\u01b0\u01a1ng tr\u00ecnh hi\u1ec3n nhi\u00ean s\u1ebd tr\u1edf th\u00e0nh ax + 0 = c, t\u1ee9c l\u00e0 ax = 0 hay x = c\/a v\u00e0 l\u00fac n\u00e0y, \u0111\u01b0\u1eddng th\u1eb3ng song song ho\u1eb7c tr\u00f9ng v\u1edbi tr\u1ee5c tung.<\/p>\n\n\n\n N\u1ebfu a = 0 v\u00e0 b # 0, th\u00ec ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n tr\u1edf th\u00e0nh 0 + by = c, t\u1ee9c l\u00e0 by = c, suy ra c = b\/y. L\u00fac n\u00e0y, \u0111\u01b0\u1eddng th\u1eb3ng (d) song song ho\u1eb7c tr\u00f9ng v\u1edbi tr\u1ee5c ho\u00e0nh.<\/p>\n\n\n\n \u0110\u00f3 l\u00e0 ba tr\u01b0\u1eddng h\u1ee3p bi\u1ec3u di\u1ec5n t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n m\u00e0 c\u00e1c em c\u1ea7n l\u01b0u \u00fd. M\u1ed7i tr\u01b0\u1eddng h\u1ee3p s\u1ebd c\u00f3 c\u00e1ch minh h\u1ecda t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh kh\u00e1c nhau.<\/p>\n\n\n\n H\u1ec7 hai ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<\/p>\n\n\n\n Ch\u00fang ta \u0111\u00e3 hi\u1ec3u ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t m\u1ed9t \u1ea9n \u0111\u01b0\u1ee3c vi\u1ebft nh\u01b0 th\u1ebf n\u00e0o r\u1ed3i, th\u00ec \u1edf \u0111\u00e2y s\u1ebd c\u00f3 c\u00f4ng th\u1ee9c nh\u01b0 sau:<\/p>\n\n\n\n Trong \u0111\u00f3, a, b, c, a\u2019, b\u2019, c\u2019 \u2282 R.<\/p>\n\n\n\n Kh\u00e1c v\u1edbi vi\u1ec7c minh h\u1ecda t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh, h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1ee3c minh h\u1ecda nh\u01b0 sau. Ch\u00fang ta s\u1ebd c\u00f3 2 \u0111\u01b0\u1eddng th\u1eb3ng (d) v\u00e0 (d\u2019) cho 2 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t ax + by = c v\u00e0 a\u2019x + b\u2019y = c. L\u00fac n\u00e0y, c\u0169ng c\u00f3 3 tr\u01b0\u1eddng h\u1ee3p x\u1ea3y ra:<\/p>\n\n\n\n (d) \/\/ (d\u2019) th\u00ec h\u1ec7 v\u00f4 nghi\u1ec7m<\/p>\n\n\n\n (d) c\u1eaft (d\u2019) th\u00ec h\u1ec7 c\u00f3 m\u1ed9t nghi\u1ec7m duy nh\u1ea5t<\/p>\n\n\n\n (d) tr\u00f9ng (d\u2019) th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m<\/p>\n\n\n\n N\u1ebfu c\u00e1c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 c\u00f9ng t\u1eadp h\u1ee3p nghi\u1ec7m th\u00ec l\u00fac n\u00e0y ch\u00fang ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u01b0\u01a1ng \u0111\u01b0\u01a1ng. Vi\u1ec7c ph\u01b0\u01a1ng tr\u00ecnh t\u01b0\u01a1ng \u0111\u01b0\u01a1ng c\u0169ng ch\u00ednh t\u1ecf c\u00e1c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00f3 c\u00f3 c\u00f9ng t\u1eadp h\u1ee3p nghi\u1ec7m. \u0110\u00e2y l\u00e0 k\u1ebft qu\u1ea3 2 chi\u1ec1u.<\/p>\n\n\n\n C\u00e1ch gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf<\/p>\n\n\n\n C\u00f3 2 c\u00e1ch gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ph\u1ed5 bi\u1ebfn, ch\u00ednh l\u00e0 d\u00f9ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf v\u00e0 ph\u01b0\u01a1ng ph\u00e1p c\u1ed9ng. Trong n\u1ed9i dung b\u00e0i h\u1ecdc h\u00f4m nay, ch\u00fang ta ch\u1ec9 t\u1eadp trung \u0111i chuy\u00ean s\u00e2u v\u1ec1 gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf l\u1edbp 9 c\u00e1c em nh\u00e9.<\/p>\n\n\n\n C\u00e1c quy t\u1eafc v\u00e0 b\u01b0\u1edbc gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf<\/p>\n\n\n\n Quy t\u1eafc th\u1ebf<\/p>\n\n\n\n C\u00e1c em c\u1ea7n n\u1eafm r\u00f5 quy t\u1eafc n\u00e0y \u0111\u1ec3 \u00e1p d\u1ee5ng v\u00e0o t\u1eebng b\u00e0i th\u1ef1c h\u00e0nh c\u1ee5 th\u1ec3. Quy t\u1eafc th\u1ebf ch\u00ednh l\u00e0 d\u00f9ng \u0111\u1ec3 bi\u1ebfn \u0111\u1ed5i m\u1ed9t h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh th\u00e0nh m\u1ed9t h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u01b0\u01a1ng \u0111\u01b0\u01a1ng.<\/p>\n\n\n\n \u0110\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c, ch\u00fang ta th\u1ef1c hi\u1ec7n qua 2 b\u01b0\u1edbc sau:<\/p>\n\n\n\n B\u01b0\u1edbc 1: V\u1edbi h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t 2 \u1ea9n \u0111\u00e3 cho, ta bi\u1ec3u di\u1ec5n m\u1ed9t \u1ea9n theo \u1ea9n kia r\u1ed3i th\u1ebf v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 2 \u0111\u1ec3 cho ra m\u1ed9t h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh m\u1edbi. L\u00fac n\u00e0y, h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau khi th\u1ebf \u0111\u00e3 ch\u1ec9 c\u00f2n 1 \u1ea9n.<\/p>\n\n\n\n B\u01b0\u1edbc 2: Sau khi \u0111\u00e3 c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh 1 \u1ea9n, ch\u00fang ta s\u1eed d\u1ee5ng n\u00f3 \u0111\u1ec3 thay th\u1ebf cho ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 hai trong h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh. Ph\u01b0\u01a1ng tr\u00ecnh th\u1ee9 nh\u1ea5t c\u0169ng th\u01b0\u1eddng \u0111\u01b0\u1ee3c thay th\u1ebf b\u1edfi h\u1ec7 th\u1ee9c bi\u1ec3u di\u1ec5n m\u1ed9t \u1ea9n theo \u1ea9n kia c\u00f3 \u0111\u01b0\u1ee3c \u1edf b\u01b0\u1edbc l\u00e0m \u0111\u1ea7u ti\u00ean.<\/p>\n\n\n\n C\u00e1ch gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf<\/p>\n\n\n\n To\u00e1n 9 gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf v\u1edbi c\u00e1c b\u01b0\u1edbc c\u01a1 b\u1ea3n sau:<\/p>\n\n\n\n B\u01b0\u1edbc 1: S\u1eed d\u1ee5ng quy t\u1eafc th\u1ebf \u0111\u00e3 n\u00eau \u1edf tr\u00ean \u0111\u1ec3 bi\u1ebfn \u0111\u1ed5i ph\u01b0\u01a1ng tr\u00ecnh b\u00e0i to\u00e1n \u0111\u00e3 cho th\u00e0nh m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh m\u1edbi, trong \u0111\u00f3, l\u01b0u \u00fd l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y c\u00f3 m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh m\u1ed9t \u1ea9n.<\/p>\n\n\n\n B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh m\u1ed9t \u1ea9n v\u1eeba c\u00f3. C\u00e1ch gi\u1ea3i c\u00e1c em \u0111\u00e3 \u0111\u01b0\u1ee3c h\u1ecdc \u1edf b\u00e0i h\u1ecdc tr\u01b0\u1edbc r\u1ed3i. Sau \u0111\u00f3, ch\u00fang ta t\u00ecm \u0111\u01b0\u1ee3c nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho. K\u1ebft qu\u1ea3 t\u00ecm nghi\u1ec7m ch\u00ednh l\u00e0 \u0111\u00e1p \u00e1n c\u1ee7a b\u00e0i to\u00e1n gi\u1ea3i h\u1ec7 pt b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf.<\/p>\n\n\n\n C\u00e1c em c\u1ea7n l\u01b0u \u00fd l\u00e0 trong qu\u00e1 tr\u00ecnh gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p n\u00e0y, ta th\u1ea5y xu\u1ea5t hi\u1ec7n ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 c\u00e1c h\u1ec7 s\u1ed1 c\u1ee7a c\u1ea3 hai \u1ea9n \u0111\u1ec1u b\u1eb1ng 0, th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 th\u1ec3 x\u1ea3y ra hai tr\u01b0\u1eddng h\u1ee3p: 1 l\u00e0 v\u00f4 nghi\u1ec7m v\u00e0 2 l\u00e0 v\u00f4 s\u1ed1 nghi\u1ec7m.<\/p>\n\n\n\n B\u00e0i t\u1eadp gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf<\/p>\n\n\n\n Nh\u01b0 v\u1eady, ch\u00fang ta v\u1eeba h\u1ecdc xong b\u00e0i gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf. \u1edf b\u00e0i n\u00e0y, c\u00e1c em \u0111\u1eb7c bi\u1ec7t l\u01b0u \u00fd \u0111\u1ebfn quy t\u1eafc th\u1ebf c\u0169ng nh\u01b0 c\u00e1c b\u01b0\u1edbc gi\u1ea3i b\u00e0i to\u00e1n nh\u00e9. C\u00e1c em c\u0169ng \u0111\u1eebng qu\u00ean m\u1ed9t s\u1ed1 tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t c\u00f3 th\u1ec3 x\u1ea3y ra. Vi\u1ec7c nh\u1edb c\u00e1c quy t\u1eafc, c\u00e1ch gi\u1ea3i s\u1ebd gi\u00fap c\u00e1c em v\u1eadn d\u1ee5ng d\u1ec5 d\u00e0ng trong c\u00e1c b\u00e0i t\u1eadp t\u01b0\u01a1ng t\u1ef1.. Ch\u00fac c\u00e1c em l\u00e0m b\u00e0i t\u1ed1t v\u00e0 \u00e1p d\u1ee5ng \u0111\u01b0\u1ee3c trong c\u00e1c b\u00e0i thi, b\u00e0i chuy\u1ec3n c\u1ea5p. H\u00e3y nh\u1edb, d\u1ea1ng b\u00e0i to\u00e1n n\u00e0y s\u1ebd c\u00f3 th\u1ec3 xu\u1ea5t hi\u1ec7n \u1edf b\u00e0i thi v\u00e0o l\u1edbp 10, n\u00ean khi \u00f4n luy\u1ec7n \u0111\u1eebng b\u1ecf qua n\u1ed9i dung b\u00e0i h\u1ecdc.<\/p>\n\n\n\n <\/p>\n\n\n\n Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<\/p>\n\n\n\n Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p c\u1ed9ng \u0111\u1ea1i s\u1ed1<\/p>\n\n\n\n Ph\u01b0\u01a1ng tr\u00ecnh quy v\u1ec1 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t b\u1eadc hai \u2013 H\u1ecdc To\u00e1n 9<\/p>\n\n\n\n C<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":" Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn To\u00e1n 9 cung c\u1ea5p cho em h\u1ecdc sinh c\u00e1c ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n v\u00e0 n\u00e2ng cao v\u1ec1 ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh. Trong n\u1ed9i dung b\u00e0i h\u1ecdc h\u00f4m nay, Vietlearn s\u1ebd h\u01b0\u1edbng d\u1eabn c\u00e1c em gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p th\u1ebf hi\u1ec7u qu\u1ea3 nh\u00e9. C\u00f9ng b\u1eaft tay […]<\/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-1101","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\/1101","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=1101"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1101\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=1101"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=1101"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=1101"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}