Solve the equation

Question

(the square root of x+2)+ (the square root of x-2)=(the square root of 4x-2)

Answer 1

√(x+2) + √(x-2) = √(4x-2)
square both sides
[√(x+2) + √(x-2)]^2 = [√(4x-2)]^2
x+2 + 2√(x^2 - 4) + x-2 = 4x - 2
2√(x^2 - 4) = 2x - 2
√(x^2 - 4) = x-1
square again
x^2 - 4 = x^2 - 2x + 1
2x = 5
x = 5/2 or 2.5

since we squared, we must check the answer in the original equation, it does work.