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受欢迎的代数 >

2x^{10}=10x^2

解答

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

解答

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}

求解步骤

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

将

10 x^{2}

para o lado esquerdo

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

因式分解

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

使用零因数法则： If

ab = 0

then

a = 0

or

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

x + 85 = 0 : x = - 85

解

x - 85 = 0 : x = 85

解

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

解

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

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}

解为

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}

作图

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