Minkowski Inequality
Algebra
Level
5
\[\large \sqrt[3]{a^3+\dfrac{1}{b^3}}+\sqrt[3]{b^3+\dfrac{1}{c^3}}+\sqrt[3]{c^3+\dfrac{1}{a^3}}\]
Given that \(a,b,c\) are positive reals satisfying \(a+b+c\le \frac{3}{2}\). Determine the minimum value of the expression above to 3 decimal places.
A solution using Minkowski Inequality will be very much appreciated!
by
Leah Jurgens