<s>[INST] 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. 
 [/INST] Hint:
$$(2-\sqrt{3})(2+\sqrt{3})=1$$
$$(2-\sqrt{3})(x)=1$$
so
$$\frac{1}{x}=2-\sqrt{3}$$
$$(x+\frac{1}{x})^2=x^2+2+\frac{1}{x^2}$$
$$x^2+\frac{1}{x^2}=(x+\frac{1}{x})^2-2$$
$$x^2+\frac{1}{x^2}=(2+\sqrt{3}+2-\sqrt{3})^2-2=14$$
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