Résoudre x^10+y=1

$$x ^ { 10 } + y = 1$$

Calculer y

$$y=1-x^{10}$$

Étapes de la solution

Soustraire x^{10} des deux côtés.

$$y=1-x^{10}$$

Calculer x (solution complexe)

$$x\in e^{\frac{\pi i}{5}}\sqrt[10]{1-y},\sqrt[10]{1-y},e^{\frac{2i\pi }{5}}\sqrt[10]{1-y},e^{\frac{3i\pi }{5}}\sqrt[10]{1-y},e^{\frac{4i\pi }{5}}\sqrt[10]{1-y},-\sqrt[10]{1-y},e^{\frac{6i\pi }{5}}\sqrt[10]{1-y},e^{\frac{7i\pi }{5}}\sqrt[10]{1-y},e^{\frac{8i\pi }{5}}\sqrt[10]{1-y},e^{\frac{9i\pi }{5}}\sqrt[10]{1-y}$$

Calculer x

$$x=\sqrt[10]{1-y}$$

$$x=-\sqrt[10]{1-y}\text{, }y\leq 1$$