Answer:
x = 2 and x = 3
Step by step explanation:
[tex]~~~~~~x = 2 +\sqrt{x-2}\\\\\implies x -2 =\sqrt{x-2}\\\\\implies (x-2)^2 = x-2 ~~~~~~~~~~~~~~~;[\text{Square both sides}]\\\\\implies x^2 -4x+4-x +2 = 0\\\\\implies x^2-5x+6 = 0\\\\\implies x^2-3x-2x+6=0\\\\\implies x(x-3)-2(x-3) = 0\\\\\implies (x-2)(x-3) = 0\\\\\implies x =2,~~x = 3\\\\\textbf{Verifying solutions:}\\\\\text{For x =2,}\\\\2= 2+\sqrt{2-2} \implies 2 = 2~ \\\\ \text{So, x = 2 is a solution.}\\\\\text{For x =3,}\\\\3 = 2+\sqrt{3-2}\implies 3=2+1 \implies 3=3\\ \\[/tex]
[tex]\text{So, x = 3 is a solution.}[/tex]
