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受欢迎的代数 >

2x^6=-19x^3-45

解答

2 x^{6} = - 19 x^{3} - 45

解答

x = - 3 \frac{9}{2}, x = - \frac{3 9 ( - 1 + 3 i )}{2 3 2}, x = - \frac{3 9 ( - 1 - 3 i )}{2 3 2}, x = - 35, x = - \frac{3 5 ( - 1 + 3 i )}{2}, x = - \frac{3 5 ( - 1 - 3 i )}{2}

求解步骤

2 x^{6} = - 19 x^{3} - 45

将

45

para o lado esquerdo

2 x^{6} + 45 = - 19 x^{3}

将

19 x^{3}

para o lado esquerdo

2 x^{6} + 45 + 19 x^{3} = 0

改写成标准形式

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

2 x^{6} + 19 x^{3} + 45 = 0

用

u = x^{3}

和

u^{2} = x^{6}

改写方程式

2 u^{2} + 19 u + 45 = 0

解

2 u^{2} + 19 u + 45 = 0 : u = - \frac{9}{2}, u = - 5

u = - \frac{9}{2}, u = - 5

代回

u = x^{3}

，求解

x

解

x^{3} = - \frac{9}{2} : x = - 3 \frac{9}{2}, x = - \frac{3 9 ( - 1 + 3 i )}{2 3 2}, x = - \frac{3 9 ( - 1 - 3 i )}{2 3 2}

解

x^{3} = - 5 : x = - 35, x = - \frac{3 5 ( - 1 + 3 i )}{2}, x = - \frac{3 5 ( - 1 - 3 i )}{2}

解为

x = - 3 \frac{9}{2}, x = - \frac{3 9 ( - 1 + 3 i )}{2 3 2}, x = - \frac{3 9 ( - 1 - 3 i )}{2 3 2}, x = - 35, x = - \frac{3 5 ( - 1 + 3 i )}{2}, x = - \frac{3 5 ( - 1 - 3 i )}{2}

作图

流行的例子

x^{3} + x^{2} - 2 x - 1 = 0

16x^4=15(x+1)^4

16 x^{4} = 15 (x + 1)^{4}

x^4+x^3+23x^2+25x-50=0

x^{4} + x^{3} + 23 x^{2} + 25 x - 50 = 0

t^{4} - t^{2} - 2 = 0

solvefor x,171y=3x^5

so l v e f or x, 171 y = 3 x^{5}