((x^5)/(x^3))^2=x

解

(\frac{x ^{5}}{x ^{3}})^{2} = x

x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

解答ステップ

(\frac{x ^{5}}{x ^{3}})^{2} = x

簡素化

(\frac{x ^{5}}{x ^{3}})^{2} : x^{4}

x^{4} = x

解く

x^{4} = x : x = 0, x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

x = 0, x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

解を検算する

未定義の (特異) 点を求める:

x = 0

equationは以下で未定義のため:

0

x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i