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受欢迎的代数 >

(2x)^4+(x^2-1)^2=-1

解答

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

解答

x = \frac{1 + 34}{34} + \frac{33}{34 \frac{1 + 34}{34}} i, x = - \frac{1 + 34}{34} - \frac{33}{34 \frac{1 + 34}{34}} i, x = \frac{1 + 34}{34} - \frac{33}{34 \frac{1 + 34}{34}} i, x = - \frac{1 + 34}{34} + \frac{33}{34 \frac{1 + 34}{34}} i

求解步骤

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

展开

(2 x)^{4} + (x^{2} - 1)^{2} : 17 x^{4} - 2 x^{2} + 1

17 x^{4} - 2 x^{2} + 1 = - 1

将

1

para o lado esquerdo

17 x^{4} - 2 x^{2} + 2 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

17 u^{2} - 2 u + 2 = 0

解

17 u^{2} - 2 u + 2 = 0 : u = \frac{1}{17} + i \frac{33}{17}, u = \frac{1}{17} - i \frac{33}{17}

u = \frac{1}{17} + i \frac{33}{17}, u = \frac{1}{17} - i \frac{33}{17}

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{1}{17} + i \frac{33}{17} : x = \frac{1 + 34}{34} + \frac{33}{34 \frac{1 + 34}{34}} i, x = - \frac{1 + 34}{34} - \frac{33}{34 \frac{1 + 34}{34}} i

解

x^{2} = \frac{1}{17} - i \frac{33}{17} : x = \frac{1 + 34}{34} - \frac{33}{34 \frac{1 + 34}{34}} i, x = - \frac{1 + 34}{34} + \frac{33}{34 \frac{1 + 34}{34}} i

解为

x = \frac{1 + 34}{34} + \frac{33}{34 \frac{1 + 34}{34}} i, x = - \frac{1 + 34}{34} - \frac{33}{34 \frac{1 + 34}{34}} i, x = \frac{1 + 34}{34} - \frac{33}{34 \frac{1 + 34}{34}} i, x = - \frac{1 + 34}{34} + \frac{33}{34 \frac{1 + 34}{34}} i

作图

流行的例子

12 x^{3} = 4

solvefor x,0.05=(1+x)^{11}-1

so l v e f or x, 0.05 = (1 + x)^{11} - 1

-w^4+60w^2-96=0

- w^{4} + 60 w^{2} - 96 = 0

12900=8700(1+x)^6

12900 = 8700 (1 + x)^{6}

solvefor r,40=x+r^4

so l v e f or r, 40 = x + r^{4}