Question

Cho \(\dfrac{a}{b}=\dfrac{c}{d}.\) Chứng minh \(\dfrac{(a+c)^2}{(b+d)^2}=\dfrac{a.c}{b.d}\).

Answer 1

\(\dfrac{a}{b}=\dfrac{c}{d}=k=\dfrac{a+c}{b+d}\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{a.c}{b.d}=k.k=k^2\\\dfrac{\left(a+c\right)^2}{\left(b+d\right)^2}=k^2\end{matrix}\right.\)

\(\Rightarrow\dfrac{\left(a+c\right)^2}{\left(b+d\right)^2}=\dfrac{a.c}{b.d}\left(đpcm\right)\)