A symmetric system of three equations

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archive posted 6 weeks ago

Solve the system

x + y + z = 6, x y + yz + z x = 11, x yz = 6.

Posed by School algebra

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$x$ , $y$ , $z$ are $1$ , $2$ , $3$ in some order, six solutions in all.

History and references

By Vieta's formulas $x$ , $y$ and $z$ are the three roots of $t^{3} - 6 t^{2} + 11 t - 6 = 0$ , which factors as $(t - 1) (t - 2) (t - 3)$ .

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