Question

Biết \(\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{ab}{cd}\) (a,b,c,d \(\ne\) 0). CMR : \(\dfrac{a}{b}=\dfrac{c}{d}\) hoặc \(\dfrac{a}{b}=\dfrac{d}{c}\)

Answer 1

Ta có :

\(\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{ab}{cd}\)

\(\Leftrightarrow\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{a^2}{c^2}=\dfrac{b^2}{d^2}\)\(\Leftrightarrow\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{ab}{cd}\)

\(\Leftrightarrow\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{ab}{cd}\)

\(\Leftrightarrow\dfrac{a}{c}=\dfrac{b}{d}\)

\(\Leftrightarrow\dfrac{a}{b}=\dfrac{c}{d}\left(đpcm\right)\)