Question-89795

Question Number 89795 by A8;15: last updated on 19/Apr/20

Answered by MJS last updated on 19/Apr/20

(x^{2} + 1) {(x + 1)}^{2} + x^{2} = {(x^{2} + x + 1)}^{2}

x^{2} (x^{2} + 1) + 1 = (x^{2} - x + 1) (x^{2} + x + 1)

\Rightarrow

\frac{x^{2} + x + 1}{x^{2} - x + 1} = x + \frac{1}{x}

x^{4} - 2 x^{3} + x^{2} - 2 x + 1 = 0

(x^{2} - \sqrt{2} x - x + 1) (x^{2} + \sqrt{2} x - x + 1) = 0

and this is easy to solve

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