If a,b,c,d,e are positive numbers bounded by p and q, i.e, if they lie in [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. inequalitiesfunctioncalculusconvex-concave inequalities