Question

Cho \(b^2=ac.\).Chứng minh rằng\(\frac{a^2+b^2}{b^2+c^2}=\frac{a}{c}\)

Answer 1

Thay \(b^2=ac\)vào \(\frac{a^2+b^2}{b^2+c^2}\)ta có :

\(\frac{a^2+b^2}{b^2+c^2}=\frac{a^2+ac}{ac+c^2}=\frac{a.\left(a+c\right)}{c.\left(a+c\right)}=\frac{a}{c}\)

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

Vậy....

Answer 2

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

Answer 3

Thế \(b^2=ac\)Ta được:

   \(\frac{a^2+ac}{ac+c^2}=\frac{a.\left(a+c\right)}{c.\left(a+c\right)}=\frac{a}{c}\left(đpcm\right)\)