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受欢迎的代数 >

6x^8+6=13x^4

解答

6 x^{8} + 6 = 13 x^{4}

解答

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

求解步骤

6 x^{8} + 6 = 13 x^{4}

将

13 x^{4}

para o lado esquerdo

6 x^{8} + 6 - 13 x^{4} = 0

改写成标准形式

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

6 x^{8} - 13 x^{4} + 6 = 0

用

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

和

u^{4} = x^{8}

改写方程式

6 u^{4} - 13 u^{2} + 6 = 0

解

6 u^{4} - 13 u^{2} + 6 = 0 : u = \frac{3}{2}, u = - \frac{3}{2}, u = \frac{2}{3}, u = - \frac{2}{3}

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

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

解

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

解

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

解为

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

作图

流行的例子

x^{3} - 7 x + 4 = 0

solvefor y,x=y^3-6

so l v e f or y, x = y^{3} - 6

x^3-6x^2+13x-12=0

x^{3} - 6 x^{2} + 13 x - 12 = 0

x^2-5x=2x^3-4x^2-x+6

x^{2} - 5 x = 2 x^{3} - 4 x^{2} - x + 6

1200=600x^2(3-x)

1200 = 600 x^{2} (3 - x)