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受欢迎的代数 >

9x^3+8x^6=-1

解答

9 x^{3} + 8 x^{6} = - 1

解答

x = - \frac{1}{2}, x = \frac{1}{4} - \frac{3}{4} i, x = \frac{1}{4} + \frac{3}{4} i, x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i

求解步骤

9 x^{3} + 8 x^{6} = - 1

将

1

para o lado esquerdo

9 x^{3} + 8 x^{6} + 1 = 0

改写成标准形式

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

8 x^{6} + 9 x^{3} + 1 = 0

用

u = x^{3}

和

u^{2} = x^{6}

改写方程式

8 u^{2} + 9 u + 1 = 0

解

8 u^{2} + 9 u + 1 = 0 : u = - \frac{1}{8}, u = - 1

u = - \frac{1}{8}, u = - 1

代回

u = x^{3}

，求解

x

解

x^{3} = - \frac{1}{8} : x = - \frac{1}{2}, x = \frac{1}{4} - \frac{3}{4} i, x = \frac{1}{4} + \frac{3}{4} i

解

x^{3} = - 1 : x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i

解为

x = - \frac{1}{2}, x = \frac{1}{4} - \frac{3}{4} i, x = \frac{1}{4} + \frac{3}{4} i, x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i

作图

流行的例子

(3x^2-10x+8)(2x-b)=0

(3 x^{2} - 10 x + 8) (2 x - b) = 0

3(t^2-9)^2+16(t^2-9)=-5

3 (t^{2} - 9)^{2} + 16 (t^{2} - 9) = - 5

solvefor D,2b-hb=D^3

so l v e f or D, 2 b - hb = D^{3}

x^3-6x^2+x-6=x^2+1

x^{3} - 6 x^{2} + x - 6 = x^{2} + 1

b^{3} = 4