Question

Cho b2 = ac. Chứng minh: \(\dfrac{a^2+b^2}{b^2+c^2}=\dfrac{a}{c}\) giải thích rõ hơn đc ko

Answer 1

\(\dfrac{a^2+b^2}{b^2+c^2}\)

\(=\dfrac{a^2+ac}{ac+c^2}\)(vì b²=ac)

\(=\dfrac{a\left(a+c\right)}{c\left(a+c\right)}\)(đặt a,c ra ngoài)

\(=\dfrac{a}{c}\)(rút gọn a+c)

Answer 2

Ta có: \(\dfrac{a^2+ac}{ac+c^2}=\dfrac{a\left(a+c\right)}{c\left(a+c\right)}=\dfrac{a}{c}\)

Vậy \(\dfrac{a^2+b^2}{b^2+c^2}=\dfrac{a}{c}\)