Question 427363
√(x-2) = x-4

Take square for both sides to eliminate the root on the left side

(√(x-2))^2 = (x-4)^2

(x - 2) = x^2 - 8x + 16

x^2 - 9x + 18 = 0

From here, we can use any methods to solve the quadratic equation

I will use A.C method to factoring the left side

(x - 6)(x - 3) =0

Apply the zero product property to let each binomial to be zero

x - 6 = 0 OR x - 3 = 0

x = 6 OR x = 3

Check your answer:

If x = 6 then the left side √(6-2)= √4 = 2 and the right side is 6 - 4 = 2

If x = 3  left side √(3-2)= √1 = 1 and the right side is 3 - 4 = -1

So the ONLY solution is x = 6