Substituting the value $x=2+\sqrt{3}$ into $x^2 + 1/x^2$ My teacher gave me a question which I am not able to solve:

If $x=2+\sqrt{3}$ then find the value of $x^2 + 1/x^2$

I tried to substitute the value of x in the expression, but that comes out to be very big. 

By the Vieta formulas, $2\pm\sqrt3$ are the roots of the quadratic equation $x^2-4x+1=0$, or $$x+\frac1x=4.$$ Squaring
$$x^2+2+\frac1{x^2}=16.$$
