#1356 · Algebra · Systems

Quadratic and Linear System with Parameter

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

~15 minAnswer checked instantlyhomogeneous equationsquadratic systems

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. X. Miscellaneous Equations, Examples X.c, No. 15

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