The set of simultaneous equations with 5 variables
Source: IMO LongList 1970 - P37
May 21, 2011
algebra proposedalgebra
Problem Statement
Solve the set of simultaneous equations
\begin{align*}
v^2+ w^2+ x^2+ y^2 &= 6 - 2u, \\
u^2+ w^2+ x^2+ y^2 &= 6 - 2v, \\
u^2+ v^2+ x^2+ y^2 &= 6- 2w, \\
u^2+ v^2+ w^2+ y^2 &= 6 - 2x, \\
u^2+ v^2+ w^2+ x^2 &= 6- 2y.
\end{align*}