<s>[INST] How to use $x + \frac{1}{x} = 7$ to compute $x^2 + \frac{1}{x^2}$. I am not sure how to approach this question:

You know that $x + \frac{1}{x} = 7$. Compute $x^2 + \frac{1}{x^2}$.

I have tried adding $x + \frac{1}{x}$ to get $\frac{x^2 +1}{x}$ but can't see if this was useful or not. 
I need help in getting started.
 [/INST] Notice $\left(x + \frac{1}{x}\right)^2 = x^2 + \frac{1}{x^2} + 2$.
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