Question

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

Answer 1

The answer is option 3.

Explanation:

Firstly, we have to move the unrelated term to the other side :

`x = 2 + √(x - 2)`

`x - 2 = √(x - 2)`

Then, you have to get rid of square root by squaring both sides :

`{(x - 2)}^(2) = {( √(x - 2) )}^(2)`

`{x}^(2) - 4x + 2 = x - 2`

`{x}^(2) - 4x + 4 - x + 2 = 0`

`{x}^(2) - 5x + 6 = 0`

Next, you have to solve it :

`{x}^(2) - 5x + 6 = 0`

`{x}^(2) - 2x - 3x + 6 = 0`

`x(x - 2) - 3(x - 2) = 0`

`(x - 2)(x - 3) = 0`

`x - 2 = 0 \\ x = 2`

`x - 3 = 0 \\ x = 3`

Answer 2

C

Explanation:

`x=2+√(x-2) \\\\x-2=√(x-2) \\\\(x-2)^2=\pm(x-2) \\\\x^2-4x+4=\pm(x-2) \\\\`

`x^2-5x+6=0` OR
`x^2+3x+2=0`

x=2 and 3

Hope this helps!