Ҳар як масъалаи математикиро ҳал кунед

Қадами ба қадам

1. x^{5} - x - 1 = 0

   Start from the equation as given.

2. x^{5} - x - 1 = 0

   The polynomial has degree 5 and no rational factors; the roots come from the general solution.

3. x = \operatorname{CRootOf} {\left(x^{5} - x - 1, 0\right)} \approx 1.1673 ,\; x = \operatorname{CRootOf} {\left(x^{5} - x - 1, 1\right)} ,\; x = \operatorname{CRootOf} {\left(x^{5} - x - 1, 2\right)} ,\; x = \operatorname{CRootOf} {\left(x^{5} - x - 1, 3\right)} ,\; x = \operatorname{CRootOf} {\left(x^{5} - x - 1, 4\right)}

   All 5 roots.

4. x \approx 1.16730309 ,\; x \approx -0.764884 - 0.35247135 i ,\; x \approx -0.764884 + 0.35247135 i ,\; x \approx 0.18123245 - 1.08395386 i ,\; x \approx 0.18123245 + 1.08395386 i

   The exact forms are unwieldy (Cardano-style radicals); here they are numerically.