Question

Resolva a seguinte equação quadrática  x²+(a+b)x+ab=0

Answer 1

Olá, Juciane.

$x\²+(a+b)x+ab=0\\\\ \Delta=(a+b)^2-4ab=a^2+2ab+b^2-4ab=a^2-2ab+b^2=(a-b)^2\\\\ x= \frac{-(a+b)\pm\sqrt\Delta}{2} =\frac{-a-b\pm\sqrt{(a-b)^2}}{2} =\frac{-a-b\pm(a-b)}{2}\Rightarrow\\\\ x_1= \frac{-a-b+(a-b)}{2} = \frac{-a-b+a-b}{2}= \frac{-2b}{2}\Rightarrow \boxed{x_1=-b}\\\\ x_2= \frac{-a-b-(a-b)}{2} = \frac{-a-b-a+b}{2}= \frac{-2a}{2}\Rightarrow \boxed{x_2=-a}\\\\ \boxed{S=\{-a,-b\}}$