Solve x^2>1/2

$$x ^ { 2 } > \frac { 1 } { 2 }$$

Solve for x

$$x\in \left(-\infty,-\frac{\sqrt{2}}{2}\right)\cup \left(\frac{\sqrt{2}}{2},\infty\right)$$

Solution Steps

Calculate the square root of \frac{1}{2} and get \frac{\sqrt{2}}{2}. Rewrite \frac{1}{2} as \left(\frac{\sqrt{2}}{2}\right)^{2}.

$$x^{2}>\left(\frac{\sqrt{2}}{2}\right)^{2}$$

Inequality holds for |x|>\frac{\sqrt{2}}{2}.

$$|x|>\frac{\sqrt{2}}{2}$$

Rewrite |x|>\frac{\sqrt{2}}{2} as x<-\frac{\sqrt{2}}{2}\text{; }x>\frac{\sqrt{2}}{2}.

$$x<-\frac{\sqrt{2}}{2}\text{; }x>\frac{\sqrt{2}}{2}$$