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人気のある代数 >

y-y^9=0

解

y - y^{9} = 0

解

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

解答ステップ

y - y^{9} = 0

因数

y - y^{9} : - y (y^{2} + 2 y + 1) (y^{2} - 2 y + 1) (y^{2} + 1) (y + 1) (y - 1)

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

零因子の原則を使用:

ab = 0

ならば

a = 0

または

b = 0

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

解く

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

解く

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

解く

y^{2} + 1 = 0 : y = i, y = - i

解く

y + 1 = 0 : y = - 1

解く

y - 1 = 0 : y = 1

解答は

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

グラフ

人気の例

x^4-48x^2+512=0

x^{4} - 48 x^{2} + 512 = 0

3x^3+2x^2-7x+2=0

3 x^{3} + 2 x^{2} - 7 x + 2 = 0

x^{7} = 0

4 x^{3} - 24 x^{2} = 0

(x^2-6)^2-3(x^2-6)-4=0

(x^{2} - 6)^{2} - 3 (x^{2} - 6) - 4 = 0