L\u00fd thuy\u1ebft v\u1ec1 ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t ba \u1ea9n – B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng<\/h2>\n

\n
1. \n

   Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t ba \u1ea9n<\/h3>\n<\/li>\n<\/ol>\n

   Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t ba \u1ea9n c\u00f3 d\u1ea1ng t\u1ed5ng qu\u00e1t l\u00e0:<\/p>\n

   ax + by + cz = d<\/p>\n

   Trong \u0111\u00f3:<\/p>\n

   x, y, z l\u00e0 3 \u1ea9n<\/p>\n

   a, b, c, d l\u00e0 c\u00e1c h\u1ec7 s\u1ed1 v\u00e0 a, b, c, d kh\u00f4ng \u0111\u1ed3ng th\u1eddi b\u1eb1ng 0.<\/p>\n

   V\u00ed d\u1ee5:<\/p>\n

   2x + y + z = 0<\/p>\n

   x – y = 6<\/p>\n

   3y = 5<\/p>\n

   \n
   1. \n

      H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t ba \u1ea9n<\/h3>\n<\/li>\n<\/ol>\n

      H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t ba \u1ea9n c\u00f3 d\u1ea1ng t\u1ed5ng qu\u00e1t l\u00e0:<\/p>\n

      Trong \u0111\u00f3 x, y, z l\u00e0 ba \u1ea9n; a_{1<\/sub>, b1<\/sub>, c1<\/sub>, a2<\/sub>, b2<\/sub>, c2, <\/sub>a3<\/sub>, b3<\/sub>, c3 <\/sub>, d1, <\/sub>d2, <\/sub>d3<\/sub> l\u00e0 c\u00e1c h\u1ec7 s\u1ed1.<\/p>\n}

      M\u1ed7i b\u1ed9 ba s\u1ed1 ( x_{0<\/sub>, y0<\/sub>, z0<\/sub> ) nghi\u1ec7m \u0111\u00fang c\u1ea3 ba ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 m\u1ed9t nghi\u1ec7m c\u1ee7a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (4).<\/p>\n}

      \n
      1. \n

         Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t ba \u1ea9n<\/h3>\n<\/li>\n<\/ol>\n

         Gia\u1ec9 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (4) l\u00e0 t\u00ecm t\u1ea5t c\u1ea3 c\u00e1c b\u1ed9 ba s\u1ed1 (x, y, z) \u0111\u1ed3ng th\u1eddi nghi\u1ec7m \u0111\u00fang c\u1ea3 3 ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u1ec7.<\/p>\n

         Nguy\u00ean t\u1eafc chung \u0111\u1ec3 gi\u1ea3i c\u00e1c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh nhi\u1ec1u \u1ea9n l\u00e0 kh\u1eed b\u1edbt \u1ea9n \u0111\u1ec3 quy v\u1ec1 gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 \u00edt \u1ea9n s\u1ed1 h\u01a1n.<\/p>\n

         \u0110\u1ec3 kh\u1eed b\u1edbt \u1ea9n, ta c\u0169ng c\u00f3 th\u1ec3 d\u00f9ng c\u00e1c ph\u01b0\u01a1ng ph\u00e1p c\u1ed9ng \u0111\u1ea1i s\u1ed1 hay ph\u01b0\u01a1ng ph\u00e1p th\u1ebf gi\u1ed1ng nh\u01b0 \u0111\u1ed1i v\u1edbi h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n.<\/p>\n

         V\u00ed d\u1ee5 1<\/strong><\/em>: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau:<\/p>\n

         <\/p>\n

         B\u00e0i gi\u1ea3i<\/em><\/p>\n

         – Th\u1ebf z = 2 v\u00e0o pt (2) ta \u0111\u01b0\u1ee3c 2y + 2 = 4 <=> 2y = 2 <=> y = 1<\/p>\n

         – Th\u1ebf z = 2, y = 1 v\u00e0o pt(1) ta \u0111\u01b0\u1ee3c x – 1 – 2 = -5 <=> x = -2<\/p>\n

         V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 nghi\u1ec7m l\u00e0: ( -2, 1, 2)<\/p>\n

         <\/p>\n

         V\u00ed d\u1ee5 2:<\/strong><\/em> Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<\/p>\n

         <\/p>\n

         Ta c\u00f3 th\u1ec3 \u0111\u01b0a h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 d\u1ea1ng tam gi\u00e1c b\u1eb1ng c\u00e1ch kh\u1eed \u1ea9n s\u1ed1 (kh\u1eed \u1ea9n x \u1edf pt(2) r\u1ed3i kh\u1eed \u1ea9n x v\u00e0 y \u1edf pt(3), …). D\u00f9ng ph\u01b0\u01a1ng ph\u00e1p c\u1ed9ng \u0111\u1ea1i s\u1ed1 gi\u1ed1ng nh\u01b0 h\u1ec7 hai ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n.<\/p>\n

         B\u00e0i gi\u1ea3i:<\/em><\/p>\n

         Tr\u1eeb t\u1eebng v\u1ebf c\u1ee7a pt(1) v\u00e0 pt(2) ta \u0111\u01b0\u1ee3c h\u1ec7 pt:<\/p>\n

         <\/p>\n

         Tr\u1eeb t\u1eebng v\u1ebf c\u1ee7a pt(1) v\u00e0 pt(3) ta \u0111\u01b0\u1ee3c h\u1ec7 pt:<\/p>\n

         <\/p>\n

         V\u1eady h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 nghi\u1ec7m l\u00e0:<\/p>\n

         <\/p>\n

         Nh\u1eadn x\u00e9t: \u0110\u1ec3 gi\u1ea3i m\u1ed9t h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t ba \u1ea9n ta th\u01b0\u1eddng bi\u1ebfn \u0111\u1ed5i hpt \u0111\u00e3 cho v\u1ec1 d\u1ea1ng tam gi\u00e1c b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p kh\u1eed d\u1ea7n \u1ea9n s\u1ed1 (ph\u01b0\u01a1ng ph\u00e1p Gau-X\u01a1 )<\/p>\n

         V\u00ed d\u1ee5 3<\/strong><\/em>: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (II) b\u1eb1ng m\u00e1y t\u00ednh b\u1ecf t\u00fai<\/p>\n

         <\/p>\n

         H\u01b0\u1edbng d\u1eabn gi\u1ea3i:<\/em><\/p>\n

         <\/p>\n

         V\u00ed d\u1ee5 4:<\/strong><\/em> Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p Gau-X\u01a1 v\u00e0 b\u1eb1ng m\u00e1y t\u00ednh b\u1ecf t\u00fai.<\/p>\n

         <\/p>\n

         Nh\u00e2n hai v\u1ebf c\u1ee7a\u00a0 pt (a) cho 2 r\u1ed3i c\u1ed9ng v\u1edbi pt (b) theo t\u1eebng v\u1ebf; nh\u00e2n hai v\u1ebf c\u1ee7a pt (a) cho (-2) r\u1ed3i c\u1ed9ng v\u1edbi pt (c) theo t\u1eebng v\u1ebf ta \u0111\u01b0\u1ee3c:<\/p>\n

         <\/p>\n

         Nh\u00e2n hai v\u1ebf c\u1ee7a pt (b’) cho 7 v\u00e0 nh\u00e2n hai v\u1ebf c\u1ee7a pt (c’) cho 5 r\u1ed3i c\u1ed9ng l\u1ea1i theo t\u1eebng v\u1ebf t\u01b0\u01a1ng \u1ee9ng ta \u0111\u01b0\u1ee3c:<\/p>\n

         <\/p>\n

          <\/p>\n

         V\u1eady nghi\u1ec7m c\u1ee7a hpt (III) l\u00e0:<\/p>\n

         <\/p>\n

         V\u00ed d\u1ee5 5.<\/strong><\/em> D\u00f9ng m\u00e1y t\u00ednh b\u1ecf t\u00fai gi\u1ea3i c\u00e1c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau:<\/p>\n

         <\/p>\n

         G\u1ee3i \u00fd :<\/strong><\/em><\/p>\n

         <\/p>\n

          <\/p>\n

         V\u00ed d\u1ee5 6. B\u00e0i t\u1eadp th\u1ef1c ti\u1ec5n<\/p>\n

         M\u1ed9t c\u1eeda h\u00e0ng b\u00e1n \u00e1o s\u01a1 mi, qu\u1ea7n \u00e2u nam v\u00e0 v\u00e1y n\u1eef. Ng\u00e0y th\u1ee9 nh\u1ea5t b\u00e1n \u0111\u01b0\u1ee3c 12 \u00e1o, 21 qu\u1ea7n v\u00e0 18 v\u00e1y, doanh thu 5.349.000 \u0111\u1ed3ng. Ng\u00e0y th\u1ee9 hai b\u00e1n \u0111\u01b0\u1ee3c 16 \u00e1o, 24 qu\u1ea7n v\u00e0 12 v\u00e1y, doanh thu l\u00e0 5.600.000 \u0111\u1ed3ng. Ng\u00e0y th\u1ee9 ba b\u00e1n \u0111\u01b0\u1ee3c 24 \u00e1o, 15 qu\u1ea7n v\u00e0 12 v\u00e1y, doanh thu 5.259.000 \u0111\u1ed3ng. H\u1ecfi gi\u00e1 b\u00e1n m\u1ed7i \u00e1o, m\u1ed7i qu\u1ea7n v\u00e0 m\u1ed7i v\u00e1y l\u00e0 bao nhi\u00eau?<\/p>\n

         B\u00e0i gi\u1ea3i:<\/p>\n

         \u0110\u1eb7t x, y, z\u00a0 t\u01b0\u01a1ng \u1ee9ng l\u00e0 gi\u00e1 b\u00e1n c\u1ee7a m\u1ed7i \u00e1o s\u01a1 mi, m\u1ed7i qu\u1ea7n \u00e2u nam, m\u1ed7i v\u00e1y n\u1eef. ( \u0110\u01a1n v\u1ecb t\u00ednh l\u00e0 ng\u00e0n \u0111\u1ed3ng ). \u0110K: x>0, y>0, z>0<\/p>\n

         <\/p>\n

         V\u00ed d\u1ee5 7: G\u1ec9ai hpt sau:<\/p>\n

         <\/p>\n

         V\u1eady nghi\u1ec7m c\u1ee7a hpt \u0111\u00e3 cho b\u1eb1ng (x, y, z) = (2, -2, 1).<\/p>\n

         Tr\u00ean \u0111\u00e2y l\u00e0 c\u00f4ng th\u1ee9c gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t ba \u1ea9n v\u00e0 b\u00e0i t\u1eadp \u00e1p d\u1ee5ng. Ch\u00fac c\u00e1c em h\u1ecdc t\u1ed1t!<\/h4>\n

          <\/p>\n

          <\/p>\n","protected":false},"excerpt":{"rendered":"

         L\u00fd thuy\u1ebft v\u1ec1 ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t ba \u1ea9n – B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t ba \u1ea9n Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t ba \u1ea9n… <\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[448,455,408],"tags":[616,612,615,614,613],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/posts\/6825"}],"collection":[{"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/comments?post=6825"}],"version-history":[{"count":0,"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/posts\/6825\/revisions"}],"wp:attachment":[{"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/media?parent=6825"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/categories?post=6825"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/tags?post=6825"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}