37

Part of 1970 IMO Longlists

Problems(1)

The set of simultaneous equations with 5 variables

Source: IMO LongList 1970 - P37

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*}

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