Answer: a) 11
Step-by-step explanation:
[tex]\sqrt{x-2}=x-8\\\\\\\text{Square both sides:}\\(\sqrt{x-2})^2=(x-8)^2\\\\\\\text{Simplify:}\\x-2=x^2-16x+64\\\\\\\text{Subtract x and add 2 to both sides:}\\0=x^2-17x+66\\\\\\\text{Factor the quadratic equation:}\\0=(x-6)(x-11)\\\\\\\text{Apply the Zero Product Property and solve for x:}\\0=x-6\qquad 0=x-11\\x=6\qquad \qquad x=11\\\\\\\text{Verify:}\\\sqrt{6-2}=6-8\qquad \qquad \sqrt{11-2}=11-8\\\sqrt4=-2\qquad \qquad \qquad \quad \sqrt9=3\\2\neq-2\qquad \qquad \qquad \qquad 3=3[/tex]
6 is NOT a valid solution, 11 IS a valid solution
