Reciprocal quartic equation

Solve the equation $x^{4} + 1 - 3 (x^{3} + x) = 2 x^{2}$ .

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H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. X. Miscellaneous Equations, Examples X.a, No. 37

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