[tex] a+b = x\\ a\cdot b = y\\ \\ (a+b)^2 = a^2 +2ab + b^2 \Rightarrow \\ \\ \Rightarrow a^2 +b^2 = (a+b)^2 - 2ab \Rightarrow\\ \\ \Rightarrow a^2 +b^2 = x^2 -2y \\ \\ \\ (a-b)^2 = a^2 -2ab +b^2 \\ \\ (a-b)^2 = a^2 +b^2 -2ab \\ \\ (a-b)^2 = x^2 -2y -2y \\ \\ (a-b)^2 = x^2 - 4y \Big| \sqrt{\square} \\ \\ |a-b| = \sqrt{x^2 - 4y} \\ \\ \boxed{a-b = \pm \sqrt{x^2 - 4y}}[/tex]
