ANSWER:
A. 6
STEP-BY-STEP EXPLANATION:
We have the following equaton:
[tex]\sqrt{x-2}=x-4[/tex]
We solve for x:
[tex]\begin{gathered} \left(\sqrt{x-2}\right)^2=\left(x-4\right)^2 \\ \\ x-2=x^2-8x+16 \\ \\ x^2-8x+16=x-2 \\ \\ x^2-8x+16-x+2=0 \\ \\ x^2-9x+18=0 \\ \\ \left(x-3\right)\left(x-6\right)=0 \\ \\ x-3=0\rightarrow x=3 \\ \\ x-6=0\operatorname{\rightarrow}x=6 \\ \\ \text{ We check each solution, like this:} \\ \\ \sqrt{6-2}=6-4\rightarrow\sqrt{4}=2\rightarrow2=2\rightarrow\text{ True} \\ \\ \sqrt{3-2}=3-4\rightarrow\sqrt{1}=-1\rightarrow1=-1\rightarrow\text{ False} \end{gathered}[/tex]
That means that the only solution of the equation is x = 6.
Therefore, the correct answer is A. 6
