\(\frac{a}{b}=\frac{c}{d}\)
\(\frac{ac}{bd}=\frac{a^2+c^2}{b^2+d^2}\)
Ta có :
\(\frac{a}{b}=\frac{c}{d}=m\Rightarrow a=m.b;c=m.d\)
\(\Rightarrow\frac{ac}{bd}=\frac{m.b.m.d}{bd}=m.m=m^2\)
\(\Rightarrow\frac{a^2+c^2}{b^2+d^2}=\frac{\left(mb\right)^2+\left(md\right)^2}{b^2+d^2}=\frac{m^2\left(b^2+d^2\right)}{b^2+d^2}=m^2\)
Vì \(m^2=m^2\Rightarrow\frac{ac}{bd}=\frac{a^2+c^2}{b^2+d^2}\)