Question

Solve the following inequality:
$(x^2-1)\sqrt{x^2-x-2}⩾0$

Answer 1

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

$(x-2)(x+1)\ge 0$

$x\in (-\infty ,-1)\cup (2,\infty )$

$(x^2-1)\sqrt{x^2-x-2}\ge 0$

squaring both sides

$(x^2-1{)}^2(x-2\left)\right(x-1)\ge 0$

$(x-1)(x-2)(x+1{)}^3\ge 0$

$x\in (-1,1)\cup (2,\infty )$