Question

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

Answer 1

Answer:

The answer is option 3.

Step-by-step explanation:

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

$x = 2 + \sqrt{x - 2}$

$x - 2 = \sqrt{x - 2}$

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

${(x - 2)}^{2} = {( \sqrt{x - 2} )}^{2}$

${x}^{2} - 4x + 2 = x - 2$

${x}^{2} - 4x + 4 - x + 2 = 0$

${x}^{2} - 5x + 6 = 0$

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

Answer:

C

Step-by-step explanation:

$x=2+\sqrt{x-2} \\\\x-2=\sqrt{x-2} \\\\(x-2)^2=\pm(x-2) \\\\x^2-4x+4=\pm(x-2)$

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

x=2 and 3

Hope this helps!