Toán Lớp 7: cho a/b=c/d. chứng minh a^2-b^2/c^2-d^2=ad/cd

Question

Toán Lớp 7:  cho a/b=c/d. chứng minh a^2-b^2/c^2-d^2=ad/cd

thanoanghha · Answer

Lời giải và giải thích chi tiết:   Đặt a/b=c/d=k   &rArr;a=bk,c=dk   ta c&oacute; a&sup2;-b&sup2;/c&sup2;-d&sup2;=(bk)&sup2;-b&sup2;/(dk)&sup2;-d&sup2;   =b&sup2;k&sup2;-b&sup2;=d&sup2;k&sup2;-d&sup2;   =b&sup2;(k&sup2;-1)/d&sup2;(k&sup2;-1)   =b&sup2;/d&sup2;   =(b/d)&sup2;   ta c&oacute; (ab/cd)&sup2;=[b(k+1)/d(k+1)]&sup2;=(b/d)&sup2;   &rArr;(ab/cd)&sup2;=a&sup2;-b&sup2;/c&sup2;-d&sup2;

lanthuhoa · Answer

Đặt a/b=c/d=k(k &ne;0 )   &rArr;a=bk,c=dk   ta c&oacute; a&sup2;-b&sup2;/c&sup2;-d&sup2;=(bk)&sup2;-b&sup2;/(dk)&sup2;-d&sup2;   =b&sup2;k&sup2;-b&sup2;=d&sup2;k&sup2;-d&sup2;   =b&sup2;(k&sup2;-1)/d&sup2;(k&sup2;-1)   =b&sup2;/d&sup2;   =(b/d)&sup2;   ta c&oacute; (ab/cd)&sup2;=[b(k+1)/d(k+1)]&sup2;=(b/d)&sup2;   &rArr;(ab/cd)&sup2;=a&sup2;-b&sup2;/c&sup2;-d&sup2;