Ta có: \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=K\)
\(\Rightarrow a=cK;b=dK\)
Khi đó: \(\frac{a^2+c^2}{b^2+d^2}=\frac{\left(cK\right)^2+c^2}{\left(dK\right)^2+d^2}=\frac{c^2.K^2+c^2}{d^2.K^2+d^2}=\frac{c^2\left(K^2+1\right)}{d^2\left(K^2+1\right)}=\frac{c^2}{d^2}=\frac{ac}{bd}\)(Do \(\frac{a}{b}=\frac{c}{d}\))
Vậy: \(\frac{ac}{bd}=\frac{a^2+c^2}{b^2+d^2}\)
sr mn chỗ cuối tôi viết nhầm ko f là \(\frac{a^2+c^2}{b^2=d^2}\) mà là: \(\frac{a^2+c^2}{b^2+d^2}\)