Question

If $\left[\frac{[1-{\left(\frac{a}{b}\right)}^{-2}]a^2}{(\sqrt{a}-\sqrt{b}{)}^2+2\sqrt{ab}}\right]=1$ and $a+b=5,$ then find $a$ and $b$.

Answer 1

$\frac{[1-{\left(\frac{a}{b}\right)}^{-2}]a^2}{(\sqrt{a}-\sqrt{b}{)}^2+2\sqrt{ab}}=1$

$\Rightarrow \frac{[1-{\left(\frac{b}{a}\right)}^2]a^2}{(a+b)}=1$

$\Rightarrow \frac{[a^2-b^2]}{(a+b)}=1$

$\Rightarrow a-b=1$ ....(1)
Given, $a+b=5$ ....(2)
On solving eq (1) and (20, we get $a=3,b=2$