#1355 · Algebra · Systems

Symmetric Cubic System

Solve the following system of equations for $x, y, z$ : $x^{3} + y^{3} + z^{3} = a^{3}$ , $x^{2} + y^{2} + z^{2} = a^{2}$ , $x + y + z = a$ .

~10 minAnswer checked instantlysymmetric polynomialspower sums

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. X. Miscellaneous Equations, Examples X.c, No. 14

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).