Question

Como resolvo |x²-x-2|=2x+2 ?

para x diferente de 0

Answer 1

$|x^2-x-2|=2x+2\\\\x^2-x-2=2x+2\ ou\ x^2-x-2=-(2x+2)\\\\x^2-x-2-2x-2=0\ ou\ x^2-x-2=-2x-2\\\\x^2-3x-4=0\ ou\ x^2+x=0\\\\\\x^2-3x-4=0\\\\\Delta=9+16=25\\\\x=\dfrac{3\pm5}{2}\\\\x=4\ ou\ x=-1\\\\\\x^2+x=0\\\\x(x+1)=0\\\\x=0\\\\x+1=0\\\\x=-1\\\\\\S:\{-1,0,4\}$

Como x eh diferente de 0 entao:

$S:\{-1,4\}$