Question

Cho a/b=c/d

Chứng minh rằng: ab/cd=(a-b) ^2/(c-d) ^2

Answer 1

Đặt :

\(\frac{a}{b}=\frac{c}{d}=k\)

\(\Leftrightarrow\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)

Ta có :

+) \(\frac{ab}{cd}=\frac{bk.b}{dk.d}=\frac{b^2k}{d^2k}=\frac{b^2}{d^2}\left(1\right)\)

+) \(\frac{\left(a-b\right)^2}{\left(c-d\right)^2}=\frac{\left(bk-b\right)^2}{\left(dk-d\right)^2}=\frac{b^2\left(k-1\right)^2}{d^2\left(k-1\right)^2}=\frac{b^2}{d^2}\left(2\right)\)

Từ \(\left(1\right)+\left(2\right)\Leftrightarrow\frac{ab}{cd}=\frac{\left(a-b\right)^2}{\left(c-d\right)^2}\left(đpcm\right)\)