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ab + c + d = 3, bc + d + a = 5, cd + a + b = 2, da + b + c = 6

Source: 2021 JBMO TST Bosnia and Herzegovina P1

October 7, 2022
algebrasystem of equations

Problem Statement

Determine all real numbers a,b,c,da, b, c, d for which ab+c+d=3ab + c + d = 3 bc+d+a=5bc + d + a = 5 cd+a+b=2cd + a + b = 2 da+b+c=6da + b + c = 6
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