calculus

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

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  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.

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