Question

√a + √b / √a - √b = 1/2 

Find   a² + ab + b² / a² - ab + b²

Could anybody, help me solve this problem ?/

Answer 1

I think there is a small error in the given problem. √a-√b  / √a+b  = 1/2. Numerator has minus and denominator plus.

$\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}} = \frac{1}{2} \\ \\ cross-multiply\ on\ LHS\ and\ RHS\, \\ \\ 2\sqrt{a}-2\sqrt{b} = \sqrt{a}+\sqrt{b} \\ \\ \sqrt{a} = 3\sqrt{b},\ \ \ squaring \\ \\ a = 9 b \\ \\ Substitute\ in\ the\ given\ fraction\ \frac{a^2+ab+b^2}{a^2-ab+b^2}\\ \\ = \frac{81b^2+9b^2+b^2}{81b^2-9b^2+b^2} \\ \\ = \frac{91b^2}{73b^2} \\ \\ = \frac{91}{73}$

Answer 2

(√a +√b)/(√a - √b)= 1/2
2(√a +√b)=(√a - √b) 
√a = -3√b
squaring
a = 9b
so 
a² + ab + b² / a² - ab + b²
(a² + 2ab + b² -ab) / (a² - 2ab + b² +ab)
= ((a+ b)² -ab) / ((a - b)² +ab)
= (100b² - 9b²) /(81b² + 9b²)
cancelling b²
= (100 - 9)/(64 + 9)
= 91/73 (ANSWER)