$\\$
`(a^2 + b^2)/(c^2 +d^2)=(ab)/(cd)`
`-> (a^2 + b^2) . cd = (c^2 +d^2) . ab`
`-> a^2cd + b^2cd=abc^2 + abd^2`
`-> a^2cd + b^2cd - abc^2 - abd^2=0`
`-> (a^2cd - abc^2) + (b^2cd - abd^2)=0`
`-> ac (ad - bc) + bd (bc - ad)=0`
`-> ac (ad-bc) - bd (ad - bc)=0`
`-> (ad-bc) (ac-bd)=0`
`->` \(\left[ \begin{array}{l}ad-bc=0\\ac-bd=0\end{array} \right.\) $\\$ `->` \(\left[ \begin{array}{l}ad=bc\\ac=bd\end{array} \right.\) $\\$ `->` \(\left[ \begin{array}{l}\dfrac{a}{b}=\dfrac{c}{d}\\\dfrac{a}{b}=\dfrac{d}{c}\end{array} \right.\) (đpcm)
