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受欢迎的代数 >

1-3(x+4)^3=25

解答

1 - 3 (x + 4)^{3} = 25

解答

x = - 6, x = - 3 + 3 i, x = - 3 - 3 i

求解步骤

1 - 3 (x + 4)^{3} = 25

展开

1 - 3 (x + 4)^{3} : - 3 x^{3} - 36 x^{2} - 144 x - 191

- 3 x^{3} - 36 x^{2} - 144 x - 191 = 25

将

25

para o lado esquerdo

- 3 x^{3} - 36 x^{2} - 144 x - 216 = 0

因式分解

- 3 x^{3} - 36 x^{2} - 144 x - 216 : - 3 (x + 6) (x^{2} + 6 x + 12)

- 3 (x + 6) (x^{2} + 6 x + 12) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x + 6 = 0 or x^{2} + 6 x + 12 = 0

解

x + 6 = 0 : x = - 6

解

x^{2} + 6 x + 12 = 0 : x = - 3 + 3 i, x = - 3 - 3 i

解为

x = - 6, x = - 3 + 3 i, x = - 3 - 3 i

作图

流行的例子

\frac{x ^{3}}{3} - x = \frac{x}{3}

-3(9x^2-4)(x^2-15)=0

- 3 (9 x^{2} - 4) (x^{2} - 15) = 0

(2 x - 3)^{5} = 243

t^{3} = 64

0=12t^3-6t^2-10

0 = 12 t^{3} - 6 t^{2} - 10