Find a,b,c,d
Source: JBMO 2008 Problem 1
June 25, 2008
inequalitiesalgebrapolynomialfunctionJBMOJunior Balkanalgebra solved
Problem Statement
Find all real numbers such that \left\{\begin{array}{cc}a \plus{} b \plus{} c \plus{} d \equal{} 20, \\
ab \plus{} ac \plus{} ad \plus{} bc \plus{} bd \plus{} cd \equal{} 150. \end{array} \right.