Question

What is the solution of x equals 2 + sqrt x - 2

a.) x=2
b.)x=3
c.)x=2 or x=3
d.) no solution​

Answer 1

Answer: c. x=2 or x=3

Hope this helped! :)

Answer 2

x = 2 or x = 3

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.