# Rerstrictions of Locus

• Aug 28th 2009, 03:02 AM
xwrathbringerx
Rerstrictions of Locus
How exactly did the person determine the restrictions of the locus from x = -4(p + 4/p)?

Thanxx a lot!!!
• Aug 28th 2009, 03:30 AM
halbard
That person may have used the AM-GM inequality: $\frac{x+y}2\geq\sqrt{xy}$ if $x,y\geq0$ with equality iff $x=y$.

Thus $p+\frac 4p\geq2\sqrt{p\times\frac4p}=4$ if $p>0$.

Consequently $p+\frac4p\leq-4$ if $p<0$.