Question

Cho a/b=c/a.(a,b,c khác 0).Chứng minh b^2-c^2/a^2+c^2=b-c/c

Answer 1

a/b = c/a  =>  \(a^2=bc\)

=> bc + c^2 - a^2 -c^2 =0

<=> c(b+c)  =  a^2 +c^2

<=> (b-c)(b+c)c  = (b-c)(a^2+c^2)

=> \(\frac{\left(b-c\left(b+c\right)\right)}{a^2+c^2}=\frac{b-c}{c}\)

=> đpcm

Answer 2

Từ \(\frac{a}{b}=\frac{c}{a}\Rightarrow a^2=bc\)

\(\Rightarrow\frac{b^2-c^2}{a^2+c^2}=\frac{b^2-c^2}{bc+c^2}=\frac{\left(b-c\right)\left(b+c\right)}{c\left(b+c\right)}=\frac{b-c}{c}\)

\(\RightarrowĐPCM\)