Question

What is the solution of x=2+\sqrt(x-2) x = 2 x = 3 x = 2 or x = 3 no solution

Answer 1

$D:x\geq2\\\\ x=2+\sqrt{x-2}\\ \sqrt{x-2}=x-2\\ x-2=x^2-4x+4\\ x^2-5x+6=0\\ x^2+x-6x+6=0\\ x^2-2x-3x+6=0\\ x(x-2)-3(x-2)=0\\ (x-3)(x-2)=0\\ x=3 \vee x=2$

Answer 2

Answer:

The solution is x = 2 or x = 3  

Step-by-step explanation:

we have to find the solution of the equation

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

$x=2+\sqrt{(x-2)}\\ \\x-2=\sqrt{x-2}\\\\\text{Squaring on both sides }\\\\(x-2)^2=x-2\\\\x^2+4-4x=x-2\\\\x^2-5x+6=0\\\\x^2-2x-3x+6=0\\\\x(x-2)-3(x-2)=0\\\\(x-2)(x-3)=0\\\\x=2\text{ or }x=3$

Hence, correct option is x = 2 or x = 3