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受欢迎的代数 >

x^3=2x+4

解答

x^{3} = 2 x + 4

解答

x = 2, x = - 1 + i, x = - 1 - i

求解步骤

x^{3} = 2 x + 4

将

4

para o lado esquerdo

x^{3} - 4 = 2 x

将

2 x

para o lado esquerdo

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

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

因式分解

x^{3} - 2 x - 4 : (x - 2) (x^{2} + 2 x + 2)

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

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

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

解

x - 2 = 0 : x = 2

解

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

解为

x = 2, x = - 1 + i, x = - 1 - i

作图

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