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 brute-force:
$$(2+\sqrt3)^2+\frac1{(2+\sqrt3)^2}=\frac{(2+\sqrt3)^4+1}{(2+\sqrt3)^2}.$$
Then
$$(2+\sqrt3)^2=7+4\sqrt3,\\
(2+\sqrt3)^4=(7+4\sqrt3)^2=97+56\sqrt3,$$
$$\frac{(2+\sqrt3)^4+1}{(2+\sqrt3)^2}=\frac{98+56\sqrt3}{7+4\sqrt3}=\frac{14\cdot7+14\cdot4\sqrt3}{7+4\sqrt3}=14.$$
