Nonlinear Symmetric System

Solve the system of equations: $6 x^{4} + x^{2} y^{2} + 16 = 2 x (12 x + y^{3})$ , $x^{2} + x y - y^{2} = 4$ .

~25 minAnswer checked instantlysimultaneous equationshigher degree equations

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. X. Miscellaneous Equations, Examples X.b, No. 36

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