MathDB

Let

a

b

c

be positive reals such that a^4 \plus{} b^4 \plus{} c^4 \equal{} 3. Prove that \sum\frac1{4 \minus{} ab}\leq1, where the

\sum

sign stands for cyclic summation. Alternative formulation: For any positive reals

a

b

c

satisfying a^4 \plus{} b^4 \plus{} c^4 \equal{} 3, prove the inequality \frac{1}{4\minus{}bc}\plus{}\frac{1}{4\minus{}ca}\plus{}\frac{1}{4\minus{}ab}\leq 1.

Problem Statement