Sum of Cubes over Product System

Solve the system of equations $\frac{x ^{2}}{y} + \frac{y ^{2}}{x} = \frac{9}{2}$ and $\frac{3}{x + y} = 1$ .

~8 minAnswer checked instantlysimultaneous equationsalgebraic manipulation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. X. Miscellaneous Equations, Examples X.b, No. 17

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