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.

$x^2 + xy + y^2 = a$  ....(1)
$x + y = b$
Squaring both sides,
$x^2 + y^2 + 2xy = b^2$
$x^2 + y^2 = b^2 - 2xy$
Put value of $x^2 + y^2$ in equation (1),
$b^2 - 2xy + xy = a$
$b^2 - xy = a$
$xy = b^2 - a$
