My professor discussed in Algebra a manipulation of equations
$$x + y = 4\\ x^2 + y^2 = 12$$
to get $xy$.
I find that $xy$ is 2.
But what topic does it fall under? If I search in Google about such problems, I don't know what keywords would lead me to right stuff. I want to know if such problems belong to a formal field. Thank you.
Symmetric polynomials, I think.
More concrete: elementary symmetric polynomials:
$$12=x^2+y^2=(x+y)^2-2xy=16-2xy.$$