How exactly did the person determine the restrictions of the locus from x = -4(p + 4/p)?

Thanxx a lot!!!

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- Aug 28th 2009, 03:02 AMxwrathbringerxRerstrictions 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 AMhalbard
That person may have used the AM-GM inequality: $\displaystyle \frac{x+y}2\geq\sqrt{xy}$ if $\displaystyle x,y\geq0$ with equality iff $\displaystyle x=y$.

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

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