Question

CHO \(B^2=AC\).

CMR:\(\frac{A^2+B^2}{B^2+C^2}=\frac{A}{C}\)

Answer 1

Từ b² = ac => \(\frac{a}{b}=\frac{b}{c}\)

Đặt \(\frac{a}{b}=\frac{b}{c}=k\)

=> \(\frac{a}{b}.\frac{b}{c}=k^2\)

=> \(\frac{a}{c}=k^2\)

Lại có: \(\frac{a^2+b^2}{b^2+c^2}=\frac{a^2}{b^2}=\frac{b^2}{c^2}=k^2\)

Mà: \(k^2=\frac{a}{c}\)

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