I have Maths test tomorrow and was just doing my revision when I came across these two questions. Would anyone please give me a nudge in the right direction?
$1)$ If $x$ is real and $y=\frac{x^2+4x-17}{2(x-3)},$ show that $|y-5|\geq2$
$2)$ If $a>0$, $b>0$, prove that $\left(a+\frac1b\right)\left(2b+\frac1{2a}\right)\ge\frac92$