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受欢迎的代数 >

x^2(x^2+4)(x^2+16)=100

解答

x^{2} (x^{2} + 4) (x^{2} + 16) = 100

解答

x = \frac{2.84044 E 15}{2.5 E 15}, x = - \frac{2.84044 E 15}{2.5 E 15}

+1

十进制

x = 1.06591 \dots, x = - 1.06591 \dots

求解步骤

x^{2} (x^{2} + 4) (x^{2} + 16) = 100

展开

x^{2} (x^{2} + 4) (x^{2} + 16) : x^{6} + 20 x^{4} + 64 x^{2}

x^{6} + 20 x^{4} + 64 x^{2} = 100

将

100

para o lado esquerdo

x^{6} + 20 x^{4} + 64 x^{2} - 100 = 0

用

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

和

u^{3} = x^{6}

改写方程式

u^{3} + 20 u^{2} + 64 u - 100 = 0

解

u^{3} + 20 u^{2} + 64 u - 100 = 0 : u \approx 1.13617 \dots, u \approx - 5.70290 \dots, u \approx - 15.43327 \dots

u \approx 1.13617 \dots, u \approx - 5.70290 \dots, u \approx - 15.43327 \dots

代回

u = x^{2}

，求解

x

解

x^{2} = 1.13617 \dots : x = \frac{2.84044 E 15}{2.5 E 15}, x = - \frac{2.84044 E 15}{2.5 E 15}

解

x^{2} = - 5.70290 \dots : x \in R

无解

解

x^{2} = - 15.43327 \dots : x \in R

无解

解为

x = \frac{2.84044 E 15}{2.5 E 15}, x = - \frac{2.84044 E 15}{2.5 E 15}

作图

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