Prove that if a1,a2,…,an, b1,b2,…,bn are arbitrary taken real numbers and c1,c2,…,cn
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}. integrationcalculusderivativeinequalities proposedinequalities