Question

If $a,b,c$ be in $G.P.,$ then prove that $\frac{a^2+ab+b^2}{bc+ca+ab}=\frac{b+a}{c+b}$

Answer 1

$b=ar,c=a{r}^2$

$L.H.S.=\frac{a^2[1+r+r^2]}{a^2[r^3+r^2+r]}=\frac{1}{r}$
$R.H.S.=\frac{a(r+1)}{a^2[r^2+r]}=\frac{1}{r}=L.H.S.$