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受欢迎的代数 >

x^9-4x^7-x^6+4x^4=0

解答

x^{9} - 4 x^{7} - x^{6} + 4 x^{4} = 0

解答

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

求解步骤

x^{9} - 4 x^{7} - x^{6} + 4 x^{4} = 0

因式分解

x^{9} - 4 x^{7} - x^{6} + 4 x^{4} : x^{4} (x + 2) (x - 2) (x - 1) (x^{2} + x + 1)

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

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

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

解

x + 2 = 0 : x = - 2

解

x - 2 = 0 : x = 2

解

x - 1 = 0 : x = 1

解

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

解为

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

作图

流行的例子

x^3-12x^2+46x-60=0

x^{3} - 12 x^{2} + 46 x - 60 = 0

0 = x^{5} - 2 x^{4} + 1

t^{3} - t^{2} - t + 1 = 0

(k^{3} - 1)^{2} = 0

a^{8} = 3