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受欢迎的代数 >

6(x-1)^3+24=-24

解答

6 (x - 1)^{3} + 24 = - 24

解答

x = - 1, x = 2 + 3 i, x = 2 - 3 i

求解步骤

6 (x - 1)^{3} + 24 = - 24

展开

6 (x - 1)^{3} + 24 : 6 x^{3} - 18 x^{2} + 18 x + 18

6 x^{3} - 18 x^{2} + 18 x + 18 = - 24

将

24

para o lado esquerdo

6 x^{3} - 18 x^{2} + 18 x + 42 = 0

因式分解

6 x^{3} - 18 x^{2} + 18 x + 42 : 6 (x + 1) (x^{2} - 4 x + 7)

6 (x + 1) (x^{2} - 4 x + 7) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x + 1 = 0 or x^{2} - 4 x + 7 = 0

解

x + 1 = 0 : x = - 1

解

x^{2} - 4 x + 7 = 0 : x = 2 + 3 i, x = 2 - 3 i

解为

x = - 1, x = 2 + 3 i, x = 2 - 3 i

作图

流行的例子

6 (x + 5)^{5} = 64

x^{3} - 0.25 x = 0

3 x^{3} - 5 = 0

(x^2-x-22)^4=4096

(x^{2} - x - 22)^{4} = 4096

x^3-2x^2-5x+3=0

x^{3} - 2 x^{2} - 5 x + 3 = 0