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受欢迎的代数 >

2(2x^4-3x^2)+2=-2x^2(x^2+2)+x^2+11

解答

2 (2 x^{4} - 3 x^{2}) + 2 = - 2 x^{2} (x^{2} + 2) + x^{2} + 11

解答

x = \frac{3}{2}, x = - \frac{3}{2}, x = i, x = - i

求解步骤

2 (2 x^{4} - 3 x^{2}) + 2 = - 2 x^{2} (x^{2} + 2) + x^{2} + 11

展开

2 (2 x^{4} - 3 x^{2}) + 2 : 4 x^{4} - 6 x^{2} + 2

展开

- 2 x^{2} (x^{2} + 2) + x^{2} + 11 : - 2 x^{4} - 3 x^{2} + 11

4 x^{4} - 6 x^{2} + 2 = - 2 x^{4} - 3 x^{2} + 11

将

11

para o lado esquerdo

4 x^{4} - 6 x^{2} - 9 = - 2 x^{4} - 3 x^{2}

将

3 x^{2}

para o lado esquerdo

4 x^{4} - 3 x^{2} - 9 = - 2 x^{4}

将

2 x^{4}

para o lado esquerdo

6 x^{4} - 3 x^{2} - 9 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

6 u^{2} - 3 u - 9 = 0

解

6 u^{2} - 3 u - 9 = 0 : u = \frac{3}{2}, u = - 1

u = \frac{3}{2}, u = - 1

代回

u = x^{2}

，求解

x

解

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

解

x^{2} = - 1 : x = i, x = - i

解为

x = \frac{3}{2}, x = - \frac{3}{2}, x = i, x = - i

作图

流行的例子

a^{3} = 64

x^3+2020x^2+20x-5=0

x^{3} + 2020 x^{2} + 20 x - 5 = 0

x^{4} = - 16 x^{2}

a^4=49+20sqrt(6)

a^{4} = 49 + 206

2 x^{6} - 17 x^{3} + 8 = 0