Question

50 pontos pra quem conseguir resolver

Resolva as equações literais:
A) x²-(a-b) x- ab=0

Answer 1

$x^2-(a-b)x-ab=0\\ \Delta=[-(a-b)]^2-4.1.(-ac)\\ \Delta=a^2-2 a b+b^2+4ac\\ \Delta=a^2+2ac+b^2\\ \Delta=(a+b)^2\\ \\ x=\frac{a-b\pm\sqrt{(a+b)^2}}{2}=\frac{a-b\pm (a+b)}{2}\\ \\ x_1=\frac{a-b-(a+b)}{2}=\frac{a-b-a-b}{2}=\frac{-2b}{2}=-b\\ \\ x_2=\frac{a-b+(a+b)}{2}=\frac{a-b+a+b}{2}=\frac{2a}{2}=a\\ \\ S=\{a,-b\}$