Question

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

Answer 1

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

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

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

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

squaring both sides

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

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

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