13(!). It is known that \(a=x+y\) and \(b=x y\) and \(c=x^{2}+y^{2}\). Find the dependence between \(a, b\) and \(c\).
13. Solution. Since \(a^{2}=(x+y)^{2}=\left(x^{2}+y^{2}\right)+2(x y)\), then \(a^{2}=c+2 b\).