Kenneth Rosen Edition 7 Exercise 1.7 Question 34 (Page No. 91)

Question

Is this reasoning for finding the solutions of the equation $\sqrt{2x^2−1=x}$ correct?

1. $\sqrt{2x^2−1=x}$ is given;
2. $2x^2−1=x^2$, obtained by squaring both sides of (1);
3. $x^2−1=0$, obtained by subtracting $x^2$from both sides of (2);
4. $(x−1)(x+1)=0$, obtained by factoring the left-hand side of$x^2−1$;
5. $x=1$ or $x=−1$,which follows because $ab=0$ implies that $a=0$ or $b=0$