Question

cho tỉ lệ thức a/b=c/d

chứng minh rằng a² - b²/c² - d² = a x b = c x d

Answer 1

\(\dfrac{a^2-b^2}{c^2-d^2}=\dfrac{ab}{cd}\) nhé :"v

Ta có: \(\dfrac{a}{b}=\dfrac{c}{d}\)

\(\Rightarrow ad=bc\)

\(\Rightarrow ad.bc=bc.bd\)

\(\Rightarrow d^2.ab=b^2.cd\)

\(\Rightarrow\dfrac{b^2}{d^2}=\dfrac{ab}{cd}\left(1\right)\)

Lại có: \(ad=bc\)

\(\Rightarrow a^2d^2=b^2c^2\)

\(\Rightarrow a^2d^2+b^2d^2=b^2c^2+b^2d^2\)

\(\Rightarrow d^2\left(a^2+b^2\right)=b^2\left(a^2+b^2\right)\)

\(\Rightarrow\dfrac{b^2}{d^2}=\dfrac{a^2-b^2}{c^2-d^2}\left(2\right)\)

Từ \(\left(1\right)\) và \(\left(2\right)\) suy ra: \(\dfrac{a^2-b^2}{c^2-d^2}=\dfrac{ab}{cd}\) ( Đpcm )