This is a problem from Regional Mathematics Olympiad, RMO 2015 Chennai Region based on the Minimal value problem. Try to solve it.
Problem: Minimal value problem
Find the minimum value of and and
Applying Arithmetic Mean – Geometric Mean Inequality (since x is positive), we have:
Hence the minimum value is 6.
- Paper: RMO 2015 (Chennai)
- What is this topic: Inequality
- What are some of the associated concepts: Arithmetic and geometric Inequality
- Where can learn these topics: Cheenta I.S.I. & C.M.I. course,Cheenta Math Olympiad Program, discuss these topics in the ‘Inequality’ module.
- Book Suggestions: Inequality by Little Mathematical Library, Secrets of Inequality