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人気のある代数 >

x^8-2x^5-3x^2=0

解

x^{8} - 2 x^{5} - 3 x^{2} = 0

解

x = 0, x = - 1, x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}, x = 33, x = - \frac{3 3}{2} + i \frac{3 3 ^{\frac{2}{3}}}{2}, x = - \frac{3 3}{2} - i \frac{3 3 ^{\frac{2}{3}}}{2}

解答ステップ

x^{8} - 2 x^{5} - 3 x^{2} = 0

因数

x^{8} - 2 x^{5} - 3 x^{2} : x^{2} (x + 1) (x^{2} - x + 1) (x - 33) (x^{2} + 33 x + 3^{\frac{2}{3}})

x^{2} (x + 1) (x^{2} - x + 1) (x - 33) (x^{2} + 33 x + 3^{\frac{2}{3}}) = 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 + 1 = 0 or x^{2} - x + 1 = 0 or x - 33 = 0 or x^{2} + 33 x + 3^{\frac{2}{3}} = 0

解く

x + 1 = 0 : x = - 1

解く

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

解く

x - 33 = 0 : x = 33

解く

x^{2} + 33 x + 3^{\frac{2}{3}} = 0 : x = - \frac{3 3}{2} + i \frac{3 3 ^{\frac{2}{3}}}{2}, x = - \frac{3 3}{2} - i \frac{3 3 ^{\frac{2}{3}}}{2}

解答は

x = 0, x = - 1, x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}, x = 33, x = - \frac{3 3}{2} + i \frac{3 3 ^{\frac{2}{3}}}{2}, x = - \frac{3 3}{2} - i \frac{3 3 ^{\frac{2}{3}}}{2}

グラフ

人気の例

x^2+5x-81=5x^5x

x^{2} + 5 x - 81 = 5 x^{5} x

20=[(5+(0.12x))/(10)]^{20}

20 = [\frac{5 + ( 0.12 x )}{10}]^{20}

y^{3} + y^{2} - 3 y - 3 = 0

(x-4)(x^2+4x+16)=-37

(x - 4) (x^{2} + 4 x + 16) = - 37

L^{3} = 1927