MathDB

4x4 system, ab + c + d = 3, bc + d + a = 5, cd + a + b = 2, da + b + c = 6

Source: Dutch IMO TST 2013 day 1 p1

August 29, 2019

algebrasystem of equations

Problem Statement

Determine all 4-tuples (

a, b,c, d

) of real numbers satisfying the following four equations:

\begin{cases} ab + c + d = 3 \\ bc + d + a = 5 \\ cd + a + b = 2 \\ da + b + c = 6 \end{cases}