Question

Resolva, em R, a equação a seguir:
(-x^2+1).(x^2-3x+2)=0

Answer 1

Olá, Jupaiva.

$(-x^2+1).(x^2-3x+2)=0 \Rightarrow \\\\\underbrace{(1+x)}_{(i)}.\underbrace{(1-x)}_{(ii)}.\underbrace{(x\²-3x+2)}_{(iii)}=0\Rightarrow\\\\\\ (i)~\boxed{x_1=-1}\\\\(ii)~\boxed{x_2=1}\\\\ (iii)~\Delta=9-8=1\Rightarrow\sqrt\Delta=1\Rightarrow x=\frac{3\pm1}{2}\Rightarrow\boxed{x_3=2}\text{ ou }\boxed{x_4=1}\\\\ \boxed{S=\{-1,1,2\}}$