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 respectively.

• A. 3,2
• B. 4,1
• C. 2,3
• D. -1,6

Answer 1

The correct option is A 3,2

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

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

$\left[\frac{(a+b)(a-b)}{(a+b)}\right]=1$
$a-b=1$...(1)
$a+b=5$...(2)
From eq (1) & (2)
$2a=6$
$a=3,b=2$