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人気のある代数 >

2x^{10}=10x^2

解

2 x^{10} = 10 x^{2}

解

x = 0, x = - 85, x = 85, x = 45 i, x = - 45 i, x = - \frac{8 5 2}{2} + i \frac{8 5 2}{2}, x = - \frac{8 5 2}{2} - i \frac{8 5 2}{2}, x = \frac{8 5 2}{2} + i \frac{8 5 2}{2}, x = \frac{8 5 2}{2} - i \frac{8 5 2}{2}

解答ステップ

2 x^{10} = 10 x^{2}

10 x^{2}

を左側に移動します

2 x^{10} - 10 x^{2} = 0

因数

2 x^{10} - 10 x^{2} : 2 x^{2} (x + 85) (x - 85) (x^{2} + 45) (x^{2} + 285 x + 45) (x^{2} - 285 x + 45)

2 x^{2} (x + 85) (x - 85) (x^{2} + 45) (x^{2} + 285 x + 45) (x^{2} - 285 x + 45) = 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 + 85 = 0 or x - 85 = 0 or x^{2} + 45 = 0 or x^{2} + 285 x + 45 = 0 or x^{2} - 285 x + 45 = 0

解く

x + 85 = 0 : x = - 85

解く

x - 85 = 0 : x = 85

解く

x^{2} + 45 = 0 : x = 45 i, x = - 45 i

解く

x^{2} + 285 x + 45 = 0 : x = - \frac{8 5 2}{2} + i \frac{8 5 2}{2}, x = - \frac{8 5 2}{2} - i \frac{8 5 2}{2}

解く

x^{2} - 285 x + 45 = 0 : x = \frac{8 5 2}{2} + i \frac{8 5 2}{2}, x = \frac{8 5 2}{2} - i \frac{8 5 2}{2}

解答は

x = 0, x = - 85, x = 85, x = 45 i, x = - 45 i, x = - \frac{8 5 2}{2} + i \frac{8 5 2}{2}, x = - \frac{8 5 2}{2} - i \frac{8 5 2}{2}, x = \frac{8 5 2}{2} + i \frac{8 5 2}{2}, x = \frac{8 5 2}{2} - i \frac{8 5 2}{2}

グラフ

人気の例

1800-1505x^2+118x^4=0

1800 - 1505 x^{2} + 118 x^{4} = 0

(x^{2} - 7) (x - 1) = 0

(x - 1)^{5} = - 32

x^{3} + 3 x - 10 = 0

9 t - t^{3} = 0