Question: Solve: \dfrac{√x +√5}{√x -√5} + \dfrac{√x -√5}{√x +√5} = 4

Solution:
Given,

\dfrac{√x +√5}{√x -√5} + \dfrac{√x -√5}{√x +√5} = 4

or, \dfrac{(√x +√5)(√x +√5) + (√x -√5)(√x -√5)}{(√x)² - (√5)²} = 4

or, \dfrac{(√x)² + 2×√x×√5 + (√5)² + (√x)² -2×√x*√5 +(√5)²}{x -5} = 4

or, x + 2\sqrt{5x} + 5 + x -2\sqrt{5x} + 5 = 4(x -5)

or, 2x +10 +0 = 4x -20

or, 20+10 = 4x -2x

or, 30 = 2x

or, 2x = 30

or, x = \dfrac{30}{2}

\therefore x = 15
= Answer