Question

cho a/b=c/d=h

C/m: ( a+b/ c+d )^2 = a^2 + b^ 2 / c^2 + d^2

Answer 1

Theo đề bài:

\(\dfrac{a}{b}=\dfrac{c}{d}=h\)

\(\Rightarrow\left\{{}\begin{matrix}a=bh\\c=dh\end{matrix}\right.\)

Khi đó:

\(\left(\dfrac{a+b}{c+d}\right)^2=\left(\dfrac{bh+b}{dh+d}\right)^2=[\dfrac{b\left(h+1\right)}{d\left(h+1\right)}]^2=\dfrac{b^2}{d^2}=\dfrac{b}{d}\)

\(\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{bh^2+b^2}{dh^2+d^2}=\dfrac{b^2\left(h^2+1\right)}{d^2\left(h^2+1\right)}=\dfrac{b^2}{d^2}=\dfrac{b}{d}\)

\(\rightarrowđpcm\)