Question

Cho \(\dfrac{a}{b}=\dfrac{c}{d}\)

CMR: \(\dfrac{a.c}{b.d}\) = \(\dfrac{a^2+c^2}{b^2+d^2}\)

Answer 1

Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\Rightarrow a=bk;c=dk\)

\(\Rightarrow\dfrac{a^2+c^2}{b^2+d^2}=\dfrac{b^2k^2+d^2k^2}{b^2+d^2}=\dfrac{k^2\left(b^2+d^2\right)}{b^2+d^2}=k^2\\ \dfrac{ac}{bd}=\dfrac{bk\cdot dk}{bd}=k^2\\ \Rightarrow\dfrac{a^2+c^2}{b^2+d^2}=\dfrac{ac}{bd}\)