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受欢迎的代数 >

x^2(x-3)=12-4x

解答

x^{2} (x - 3) = 12 - 4 x

解答

x = 3, x = 2 i, x = - 2 i

求解步骤

x^{2} (x - 3) = 12 - 4 x

展开

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

x^{3} - 3 x^{2} = 12 - 4 x

将

4 x

para o lado esquerdo

x^{3} - 3 x^{2} + 4 x = 12

将

12

para o lado esquerdo

x^{3} - 3 x^{2} + 4 x - 12 = 0

因式分解

x^{3} - 3 x^{2} + 4 x - 12 : (x - 3) (x^{2} + 4)

(x - 3) (x^{2} + 4) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

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

解

x - 3 = 0 : x = 3

解

x^{2} + 4 = 0 : x = 2 i, x = - 2 i

解为

x = 3, x = 2 i, x = - 2 i

作图

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