Question

Cho tỉ lệ thức \(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\)  CMR :  \(\frac{a}{b}=\frac{c}{d}\)

Answer 1

\(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}< =>\left(a^2+b^2\right).cd=\left(c^2+d^2\right).ab< =>\left(a^2+b^2\right).cd-\left(c^2+d^2\right).ab=0\)

\(< =>a^2cd+b^2cd-c^2ab-d^2ab=0< =>\left(a^2cd-c^2ab\right)-\left(d^2ab-b^2cd\right)=0\)

\(< =>ac\left(ad-bc\right)-bd\left(ad-bc\right)=0< =>\left(ad-bc\right)\left(ac-bd\right)=0< =>ad-bc=0< =>ad=bc< =>\frac{a}{d}=\frac{b}{c}\) (đpcm)