Question

Cho a/b=c/d .Chứng minh rằng 

a) (a-c)⁴ /(b-d)⁴ =5a⁴+7c⁴/5b⁴+7d⁴

Answer 1

Mình cần gấp ạ 

Answer 2

-Đặt \(\frac{a}{b}=\frac{c}{d}=k=>a=bk;b=dk\)

-Gọi a=bk;c=dk ta có:

\(\frac{\left(a-c\right)^4}{\left(b-d\right)^4}=\frac{\left(bk-dk\right)^4}{\left(b-d\right)^4}=\frac{k^4\left(b-d\right)^4}{\left(b-d\right)^4}=k^4\)(1)

\(\frac{5a^4+7c^4}{5b^4+7d^4}=\frac{5b^4k^4+7d^4k^4}{5b^4+7d^4}=\frac{k^4\left(5b+7d\right)^4}{\left(5b^4+7d^4\right)}=k^4\)(2)

-Từ (1)và(2)=>\(\frac{\left(a-c\right)^4}{\left(b-d\right)^4}=\frac{5a^4+7c^4}{5b^4+7d^4}\)(Điều cần chứng minh)