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受欢迎的代数 >

0.2N+0.006N^{1.6}=40

解答

0.2 N + 0.006 N^{1.6} = 40

解答

N = 128.75591 \dots, N = - 569.95374 \dots

求解步骤

0.2 N + 0.006 N^{1.6} = 40

使用以下的指数特性

: a^{n} = (a^{\frac{1}{m}})^{(n \cdot m)}

N^{1.6} = (N^{\frac{1}{5}})^{(1.6 \cdot 5)}

0.2 (N^{\frac{1}{5}})^{5} + 0.006 (N^{\frac{1}{5}})^{8} = 40

用

N^{\frac{1}{5}} = u

改写方程式

0.2 u^{5} + 0.006 u^{8} = 40

解

0.2 u^{5} + 0.006 u^{8} = 40 : u \approx 2.64212 \dots, u \approx - 3.55768 \dots

u \approx 2.64212 \dots, u \approx - 3.55768 \dots

代回

u = N^{\frac{1}{5}}

，求解

N

解

N^{\frac{1}{5}} = 2.64212 \dots : N = 128.75591 \dots

解

N^{\frac{1}{5}} = - 3.55768 \dots : N = - 569.95374 \dots

N = 128.75591 \dots, N = - 569.95374 \dots

验证解:

N = 128.75591 \dots

真

, N = - 569.95374 \dots

真

解为

N = 128.75591 \dots, N = - 569.95374 \dots

作图

流行的例子

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