find-real-solution-of-equation-x-5-x-4-1-0-

Question Number 96715 by bobhans last updated on 04/Jun/20

find real solution of equation

x^{5} + x^{4} + 1 = 0

Answered by bemath last updated on 04/Jun/20

(x^{2} + x + 1) (x^{3} - x + 1) = 0

first term nothing have real solution

the second term

x^{3} - x + 1 = 0

b y C ardano

x = \sqrt[3]{\frac{- q}{2} + \sqrt{\frac{q^{2}}{4} + \frac{p^{3}}{27}}} + \sqrt[3]{\frac{- q}{2} - \sqrt{\frac{q^{2}}{4} + \frac{p^{3}}{27}}}

x = \sqrt[3]{\frac{- 1}{2} + \sqrt{\frac{1}{4} - \frac{1}{27}}} + \sqrt[3]{\frac{- 1}{2} - \sqrt{\frac{1}{4} - \frac{1}{27}}}

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