Question

Solve the following inequalities:

$2-x-x^2\ge 0$

Answer 1

Given inequality is $2-x-x^2\ge 0$

$\Rightarrow x^2+x-2\le 0$

$\Rightarrow x^2+2x-x-2<0$

$\Rightarrow x(x+2)-1(x+2)<0$

$\Rightarrow (x+2)(x-1)<0$

$\Rightarrow (x+2)>0$ and $(x-1)<0$ or $x+2<0$ and $x-1>0$

$x<-2$ and $x<1$

$\Rightarrow -2<x<1$

Hence, $x\in (-2,1)$