ANSWER:
x = 1
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]\sqrt{2x^2-1}=x[/tex]We solve for x:
[tex]\begin{gathered} 2x^2-1=x^2 \\ \\ 2x^2-x^2=1 \\ \\ x^2=1 \\ \\ x=\sqrt{1}=\pm1 \\ \\ \text{ we check:} \\ x=1 \\ \\ \sqrt{2\left(1\right)^2-1}=1 \\ \\ \sqrt{2-1}=1 \\ \\ 1=1 \\ \\ x=-1\rightarrow\text{ true} \\ \\ \sqrt{2\left(-1\right)^2-1}=-1 \\ \\ \sqrt{2^-1}=-1 \\ \\ 1=-1\rightarrow\text{ false} \end{gathered}[/tex]Therefore, the solution of the equation is x = 1
