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受欢迎的代数 >

0=x^5-5x

解答

0 = x^{5} - 5 x

解答

x = 0, x = - 45, x = 45, x = 5 i, x = - 5 i

求解步骤

0 = x^{5} - 5 x

交换两边

x^{5} - 5 x = 0

因式分解

x^{5} - 5 x : x (x + 45) (x - 45) (x^{2} + 5)

x (x + 45) (x - 45) (x^{2} + 5) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or x + 45 = 0 or x - 45 = 0 or x^{2} + 5 = 0

解

x + 45 = 0 : x = - 45

解

x - 45 = 0 : x = 45

解

x^{2} + 5 = 0 : x = 5 i, x = - 5 i

解为

x = 0, x = - 45, x = 45, x = 5 i, x = - 5 i

作图

流行的例子

x^{4} - 6 x^{2} + 8 = D

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m^{4} - 1 = 3

3 x^{3} + 12 x = 0

4x^3-20x^2-9x+45=0

4 x^{3} - 20 x^{2} - 9 x + 45 = 0