How do I solve $x+{1\over x}=4 \Rightarrow x^2+{1 \over x^2}=?$

Question

$x+{1\over x}=4 \Rightarrow x^2+{1 \over x^2}=?$

Answer 1

$$x+\dfrac{1}{x}=4\implies (x+\dfrac{1}{x})^2=x^2+2+\dfrac{1}{x^2}=4^2=16\implies x^2+\dfrac{1}{x^2}=14$$

Answer 2

$ (x+ \frac{1}{x})^2 = (x+ \frac{1}{x})(x+ \frac{1}{x})$ = $x^2$+ $2.x.\frac{1}{x}$ + $\frac{1}{x^2}$ =$x^2$ + $\frac{1}{x^2}$ +$2$. Then just plug and chug. By the way, welcome to Mathematics stackexchange.