Question: Solve: \sqrt{x} + \sqrt{x+13} = \dfrac{91}{\sqrt{x+13}}

Solution:
Given,

 \sqrt{x} + \sqrt{x+13} = \dfrac{91}{\sqrt{x+13}}

or, \sqrt{x}  = \dfrac{91}{\sqrt{x+13}} - \sqrt{x+13}

or, \sqrt{x} = \dfrac{91 - (\sqrt{x+13})(\sqrt{x+13})}{\sqrt{x+13}}

or, \sqrt{x} (\sqrt{x + 13} = 91 - \sqrt{(x+13)^2}

or, \sqrt{x(x+13)} = 91 - (x+13)

or, \sqrt{x(x+13)} = 91 -x -13

or, \sqrt{x(x+13)} = 78 - x

Squaring both sides

or, (\sqrt{x(x+13)})^2 = (78-x)^2

or, x(x+13) = 78^2 - 2*78*x + x^2

or, x^2 + 13x = 6084 - 156 x + x^2

or, x^2 - x^2 +13x + 156c = 6084

or, 169x = 6084

or, x = \dfrac{6084}{169}

\therefore x = 36
= Answer