<s>[INST] Solve expression with unknown variables I am stuck in this next problem:

Given $x-y = 7$ and $xy = 5$, without solving for the values of $x$ and $y$, evaluate $x^2 + y^2$.

How can I solve this?
 [/INST] First expand $(x-y)^2$ to give 
\begin{align}(x-y)^2&=x^2+y^2-2xy\end{align}
We can then substitute in the values we have been given and solve the resulting equation
\begin{align}7^2&=x^2+y^2-2\times 5\\
49&=x^2+y^2-10\\
x^2+y^2&=59\end{align}
Most of the time questions like this involve you spotting an expansion of one term which involves the other term, in this case we note that squaring $x-y$ will give us an $xy$ term and some $x^2$ and $y^2$ terms so this is probably a good place to start looking.
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