Lời giải:
`(a^2+b^2)/(c^2+d^2)=(ab)/(cd)`
`-> (a^2+b^2).cd=(c^2+d^2).ab`
`-> a^2cd+b^2cd=c^2ab+d^2ab`
`-> a^2cd+b^2cd-c^2ab-d^2ab=0`
`-> (a^2cd-d^2ab)+(b^2cd-c^2ab)=0`
`-> ad(ac-db)+bc(bd-ca)=0`
`-> ad(ac-db)-bc(ca-bd)=0`
`-> (ad-bc)(ac-db)=0`
`->` \(\left[ \begin{array}{l}ad-bc=0\\ac-db=0\end{array} \right.\)
`->` \(\left[ \begin{array}{l}ad=bc\\ac=db\end{array} \right.\)
`->` \(\left[ \begin{array}{l}\frac{a}{b}=\frac{c}{d}\\\frac{a}{b}=\frac{d}{c}\end{array} \right.\) `(đpcm)`
