Question

What is the solution of x = 2 + StartRoot x minus 2 EndRoot?

Answer 1

x = 2 and x = 3

Step by step explanation:

`~~~~~~x = 2 +√(x-2)\\\\\implies x -2 =√(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+√(2-2) \implies 2 = 2~ \\\\ \text{So, x = 2 is a solution.}\\\\\text{For x =3,}\\\\3 = 2+√(3-2)\implies 3=2+1 \implies 3=3\\ \\`

`\text{So, x = 3 is a solution.}`