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Math Help - Rerstrictions of Locus

  1. #1
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    Exclamation Rerstrictions of Locus

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

    Thanxx a lot!!!
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  2. #2
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    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.
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