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受欢迎的代数 >

4x(1-x^8)=0

解答

4 x (1 - x^{8}) = 0

解答

x = 0, x = - 1, x = 1, x = i, x = - i, 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}

求解步骤

4 x (1 - x^{8}) = 0

因式分解

4 x (1 - x^{8}) : - 4 x (x + 1) (x - 1) (x^{2} + 1) (x^{2} + 2 x + 1) (x^{2} - 2 x + 1)

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

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

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

解

x + 1 = 0 : x = - 1

解

x - 1 = 0 : x = 1

解

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

解

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

解

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

解为

x = 0, x = - 1, x = 1, x = i, x = - i, 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}

作图

流行的例子

(1 + r)^{5} = 8

x^3-x^2=4x^2-8x+4

x^{3} - x^{2} = 4 x^{2} - 8 x + 4

m^{4} - 1 = 0

x - 4 = - 2 x^{3}

4x^3-3x^2+4x+11=0

4 x^{3} - 3 x^{2} + 4 x + 11 = 0