Inequality in Interval [p,q]
Source: 0
April 4, 2010
inequalitiesfunctioncalculusconvex-concave inequalities
Problem Statement
If are positive numbers bounded by and , i.e, if they lie in , 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.