Question

Cho \(\frac{a}{b}=\frac{c}{d}\)

CMR: \(\frac{ab}{cd}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)

Answer 1

đặt \(\frac{a}{b}=\frac{c}{d}=k\) => a = b.k; c = d.k

\(\frac{ab}{cd}=\frac{b^2k}{d^2.k}=\frac{b^2}{d^2}\)

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

=> \(\frac{ab}{cd}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\) ( Vì cùng bằng b²/ d² )

Answer 2

Bạn cũng có thể làm như thế này !

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

\(\rightarrow\frac{a}{b}\times\frac{b}{d}=\left(\frac{a+b}{c+d}\right)^2\)

\(\rightarrow\frac{ab}{cd}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)                      (dpcm)