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Inequality in Interval [p,q]

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April 4, 2010
inequalitiesfunctioncalculusconvex-concave inequalities

Problem Statement

If a,b,c,d,e a,b,c,d,e are positive numbers bounded by p p and q q, i.e, if they lie in [p,q],0<p [p,q], 0 < p, prove that (a \plus{} b \plus{} c \plus{} d \plus{} e)\left(\frac {1}{a} \plus{} \frac {1}{b} \plus{} \frac {1}{c} \plus{} \frac {1}{d} \plus{} \frac {1}{e}\right) \le 25 \plus{} 6\left(\sqrt {\frac {p}{q}} \minus{} \sqrt {\frac {q}{p}}\right)^2 and determine when there is equality.