Question

Cho a/c = c/b . Chứng minh rằng : a) a^2 + c^2 /b^2 + c^2 = a/b b)b^2 - a^2 / a^2 + c^2 = b-a / a

Answer 1

Ta có  : \(\frac{a}{c}=\frac{c}{b}\)

\( \implies\) \(ab=c^2\)

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

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