MathDB

Prove that if

a_{1},a_{2},\ldots,a_{n}

b_{1},b_{2},\ldots,b_{n}

are arbitrary taken real numbers and

c_{1},c_{2},\ldots,c_{n}

are positive real numbers, than \left(\sum_{i,j \equal{} 1}^{n}\frac {a_{i}a_{j}}{c_{i} \plus{} c_{j}}\right)\left(\sum_{i,j \equal{} 1}^{n}\frac {b_{i}b_{j}}{c_{i} \plus{} c_{j}}\right)\ge \left(\sum_{i,j \equal{} 1}^{n}\frac {a_{i}b_{j}}{c_{i} \plus{} c_{j}}\right)^{2}.

Problem Statement