Aram's real solutions

Algebra Level 4

The sum of all real solutions of the equation (x+1)(x1)32xx2=0\sqrt{(x+1)(x-1)^3}-2x\sqrt{x-2} =0 can be expressed as a+b+c\sqrt{a}+\sqrt{b}+\sqrt{c}, where a,b,a,b, and cc are positive integers. What is the value of a+b+ca+b+c?

This problem is posed by Aram T.

Details and assumptions

For this question, the domain of the square root function is non-negative numbers.

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