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受欢迎的代数 >

64a^6-112a^4+56a^2-7=0

解答

64 a^{6} - 112 a^{4} + 56 a^{2} - 7 = 0

解答

a = \frac{2.35319 E 15}{1.25 E 16}, a = - \frac{2.35319 E 15}{1.25 E 16}, a = \frac{3.0563 E 15}{5.0 E 15}, a = - \frac{3.0563 E 15}{5.0 E 15}, a = \frac{2.97026 E 14}{3.125 E 14}, a = - \frac{2.97026 E 14}{3.125 E 14}

+1

十进制

a = 0.43388 \dots, a = - 0.43388 \dots, a = 0.78183 \dots, a = - 0.78183 \dots, a = 0.97492 \dots, a = - 0.97492 \dots

求解步骤

64 a^{6} - 112 a^{4} + 56 a^{2} - 7 = 0

用

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

和

u^{3} = a^{6}

改写方程式

64 u^{3} - 112 u^{2} + 56 u - 7 = 0

解

64 u^{3} - 112 u^{2} + 56 u - 7 = 0 : u \approx 0.18825 \dots, u \approx 0.61126 \dots, u \approx 0.95048 \dots

u \approx 0.18825 \dots, u \approx 0.61126 \dots, u \approx 0.95048 \dots

代回

u = a^{2}

，求解

a

解

a^{2} = 0.18825 \dots : a = \frac{2.35319 E 15}{1.25 E 16}, a = - \frac{2.35319 E 15}{1.25 E 16}

解

a^{2} = 0.61126 \dots : a = \frac{3.0563 E 15}{5.0 E 15}, a = - \frac{3.0563 E 15}{5.0 E 15}

解

a^{2} = 0.95048 \dots : a = \frac{2.97026 E 14}{3.125 E 14}, a = - \frac{2.97026 E 14}{3.125 E 14}

解为

a = \frac{2.35319 E 15}{1.25 E 16}, a = - \frac{2.35319 E 15}{1.25 E 16}, a = \frac{3.0563 E 15}{5.0 E 15}, a = - \frac{3.0563 E 15}{5.0 E 15}, a = \frac{2.97026 E 14}{3.125 E 14}, a = - \frac{2.97026 E 14}{3.125 E 14}

作图

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