Toán Lớp 7: Cho a/b=c/d chứng minh rằng 7a^2+3ab/11a^2-8b^2=7c^2+3cd/11c^2-8d^2

Question

Toán Lớp 7:  Cho a/b=c/d chứng minh rằng 7a^2+3ab/11a^2-8b^2=7c^2+3cd/11c^2-8d^2

truongthanhhung · Answer

Đáp án:       Giải thích các bước giải:

kimoanh34 · Answer

Đặt (7a&sup2; + 3ab)/(11a&sup2; - 8b&sup2;) l&agrave; (1)   Đặt a/b = c/d = k      (k &isin; N*)   &rArr; a = bk; c = dk.  (*)   Thay (*) v&agrave;o (1) ta c&oacute;:   (7a&sup2; + 3ab)/(11a&sup2; - 8b&sup2;) = (7b&sup2;k&sup2; + 3b&sup2;k)/(11b&sup2;k&sup2; - 8b&sup2;)   = (b&sup2; (7k&sup2; + 3k))/(b&sup2;(11k&sup2; - 8)) = (7k&sup2; + 3k)/(11k&sup2; - 8)         (1)   Thay (*) v&agrave;o vế phải ta c&oacute;:   (7c&sup2; + 3cd)/(11c&sup2; - 8d) = (7d&sup2;k&sup2; + 3d&sup2;k)/(11d&sup2;k&sup2; - 8d&sup2;)   = (d&sup2;(7k&sup2; + 3k))/(d&sup2;(11k&sup2; - 8)) = (7k&sup2; + 3k)/(11k&sup2; - 8)          (2)   Từ (1) v&agrave; (2) suy ra:   (7a&sup2; + 3ab)/(11a&sup2; - 8b&sup2;) = (7c&sup2; + 3cd)/(11c&sup2; - 8d)