Solve for x in the equation below x^4 + 2x^3 − x^2 + 2x + 1 = 0


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Question Number 7054 by Tawakalitu. last updated on 08/Aug/16

$S o l v e f o r x i n t h e e q u a t i o n b e l o w$ $x^{4} + 2 x^{3} - x^{2} + 2 x + 1 = 0$
Commented by prakash jain last updated on 08/Aug/16

${(x^{2} + x + 1)}^{2} = x^{4} + x^{2} + 1 + 2 x^{3} + 2 x + 2 x^{2}$ $x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1$ $g i v e n e x p r - {(x^{2} + x + 1)}^{2} = - 4 x^{2} + 1$ ${(x^{2} - x + 1)}^{2} = x^{4} + x^{2} + 1 - 2 x^{3} - 2 x + 2 x^{2}$ $= x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1$ $g i v e n e x p r - {(x^{2} - x + 1)}^{2}$ $= - 4 x^{3} - 4 x^{2} - 4 x = - 4 x (x^{2} + x + 1)$ $h e n c e g i v e n e x p r$ $= {(x^{2} + x + 1)}^{2} - 4 x (x^{2} + x + 1)$ $= (x^{2} + x + 1) (x^{2} - 3 x + 1)$ $c a n b e s o l v e d a s q u a d r a t i c$
Commented by Tawakalitu. last updated on 08/Aug/16

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