Solve for xy in terms of a and b $$x^2 + xy + y^2 = a$$
$$x + y = b$$
$xy = ?$
I tried this and did this:
$xy = a - x^2 - y^2$
$xy = a - (x^2 + y^2)$
$xy = a - (x + y)(x - y)$
$xy = a - b(x - y)$
At this point I can't think of anything to do to represent the $x - y$ part in terms of $a$ and $b$.
Any help would be appreciated.

We are given \begin{align}x^2+xy+y^2&=a\tag{1}\\
x+y&=b\tag{2}\end{align}
We can square the equation $(2)$ to give us \begin{align}b^2&=(x+y)^2\\
&=x^2+2xy+y^2\end{align}
Therefore, we now have \begin{align}a&=x^2+xy+y^2\tag{1}\\
b^2&=x^2+2xy+y^2\tag{3}\end{align}
We can rearrange equation $(3)$ and substitute equation $(1)$ into it to give us the answer: \begin{align}b^2&=(x^2+xy+y^2)+xy\\
b^2&=a+xy\\
xy&=b^2-a\end{align}
