Answer:
x = 2 or x = 3
Step-by-step explanation:
x = 2 + sqrt(x - 2)
x - 2 = sqrt(x - 2) You could divide both sides by sqrt(x - 2)
sqrt(x - 2) = 1 Square both sides
x - 2 = 1 Add 2 to both sides
x = 3
There is a second way.
x - 2 = sqrt(x - 2) Square
x^2 - 4x + 4 = x - 2 Transfer x - 2 to the left
x^2 - 5x + 6 = 0 Factor
(x - 2)(x-3) = 0 Find the roots.
x - 2 = 0
x = 2
x - 3 = 0
x = 3
We have to check both results.
x = 2 + sqrt(x - 2)
2 = 2 + sqrt(2 -2)
2 = 2 + 0
2 = 2 This seems to work.
x = 2 + sqrt(x - 2)
3 = 2 + sqrt(3 - 2)
3 = 2 + sqrt(1)
3 = 2 + 1
3 = 3 And this works.
