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受欢迎的代数 >

0=2x^6-27x^4

解答

0 = 2 x^{6} - 27 x^{4}

解答

x = 0, x = \frac{3 3}{2}, x = - \frac{3 3}{2}

+1

十进制

x = 0, x = 3.67423 \dots, x = - 3.67423 \dots

求解步骤

0 = 2 x^{6} - 27 x^{4}

交换两边

2 x^{6} - 27 x^{4} = 0

用

u = x^{2}, u^{2} = x^{4}

和

u^{3} = x^{6}

改写方程式

2 u^{3} - 27 u^{2} = 0

解

2 u^{3} - 27 u^{2} = 0 : u = 0, u = \frac{27}{2}

u = 0, u = \frac{27}{2}

代回

u = x^{2}

，求解

x

解

x^{2} = 0 : x = 0

解

x^{2} = \frac{27}{2} : x = \frac{3 3}{2}, x = - \frac{3 3}{2}

解为

x = 0, x = \frac{3 3}{2}, x = - \frac{3 3}{2}

作图

流行的例子

y^5-12y^4+24y^3=0

y^{5} - 12 y^{4} + 24 y^{3} = 0

solvefor x,x^3+2x^2+x=0

so l v e f or x, x^{3} + 2 x^{2} + x = 0

s^{3} = 27

17c^1+5c^2+255c^3=53

17 c^{1} + 5 c^{2} + 255 c^{3} = 53

(2x+2)(3x-6)(4x+12)=0

(2 x + 2) (3 x - 6) (4 x + 12) = 0