Question

Cho a = b = c và \(c=\frac{bd}{b-d}\left(b\ne0;d\ne0\right)\)

Chứng minh \(\frac{a}{b}=\frac{c}{d}\)

Answer 1

Ta có :

\(c=\frac{bd}{b-d}\)

\(\Rightarrow b-d=\frac{bd}{c}\left(c\ne0\right)\)

\(a=b+c\Rightarrow c=a-b\)

\(\Rightarrow c=\frac{bd}{b-d}=a-b\)

\(\Rightarrow bd=\left(a-b\right).\left(b-d\right)\)

\(\Rightarrow ab-ad-b^2+bd=bd\)

\(\Rightarrow a\left(b-d\right)-b^2=0\)

\(\Rightarrow a.\frac{bd}{c}-b^2=0\)

\(\Rightarrow\frac{ad}{c}-b=0\)

\(\Rightarrow\frac{ad-bc}{c}=0\)

\(\Rightarrow ad-bc=0\)

\(\Rightarrow ad=bc\)

\(\Rightarrow\frac{a}{b}=\frac{c}{d}\left(đpcm\right)\)

Chúc bạn học tốt !!!