solve for x x^2 + (x^2 /((x+1)^2 )) = 3


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Question Number 169653 by infinityaction last updated on 05/May/22

$s o l v e f o r x$ $x^{2} + \frac{x^{2}}{{(x + 1)}^{2}} = 3$
	Answered by mr W last updated on 05/May/22

	$x^{2} - (3 - x^{2}) {(x + 1)}^{2} = 0$ $x^{4} + 2 x^{3} - x^{2} - 6 x - 3 = 0$ $(x^{2} - x - 1) (x^{2} + 3 x + 3) = 0$ $x^{2} - x - 1 = 0$ $\Rightarrow x = \frac{1 \pm \sqrt{5}}{2}$ $x^{2} + 3 x + 3 = 0$ $\Rightarrow x = \frac{- 3 \pm i \sqrt{3}}{2}$
	Commented by infinityaction last updated on 05/May/22

	$t h a n k y o u s i r$
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