Question

Solve the following inequality:
$|x-6|>|x^2-5x+9|.$

Answer 1

$x^2-5x+9$ has imaginary roots $⟹$ it is always positive

for $x\ge 6⟹x-6>x^2-5x+9$

$x^2-6x+15<0⟹x\in$ { } $\because$ it has imaginary roots

for $x<6⟹6-x>x^2-5x+9$

$x^2-4x+3<0⟹x\in (1,3)$