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人気のある代数 >

x^5+x=0

解

x^{5} + x = 0

解

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

解答ステップ

x^{5} + x = 0

因数

x^{5} + x : x (x^{2} + 2 x + 1) (x^{2} - 2 x + 1)

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

零因子の原則を使用:

ab = 0

ならば

a = 0

または

b = 0

x = 0 or x^{2} + 2 x + 1 = 0 or x^{2} - 2 x + 1 = 0

解く

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

解く

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

解答は

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

グラフ

人気の例

x (x + 1) (x + 2) = 0

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

m^{3} = - 1000

x^{4} - x = 1

4350=45000(1-k)^6

4350 = 45000 (1 - k)^{6}