Question

Solve the following inequality:
$x-3<\sqrt{x-2}.$

Answer 1

$x-2\ge 0$

$xϵ[2,\infty )$

$x-3<\sqrt{x-2}$

Squarring both sides

$x^2-6x+9<x-2$

$x^2-7x+11<0$

$(x-(\frac{7+\sqrt{5}}{2}\left)\right)(x-(\frac{7-\sqrt{5}}{2}\left)\right)<0$

$xϵ(\frac{7-\sqrt{5}}{2},\frac{7+\sqrt{5}}{2})$