Question

Solve the following inequality:
$\sqrt{2x-x^2}<5-x.$

Answer 1

$2x-x^2\ge 0$

$x^2-2x\le 0$

$x(x-2)\le 0$

$xϵ[0,2]$

$\sqrt{2x-x^2}<5-x$

Squarring both sides

$2x-x^2<25+x^2-10x$

$2x^2-12x+25>0$

As discriminant less than zero so $2x^2-12x+25>0$ for every $xϵR$

$xϵ[0,2]$