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受欢迎的代数 >

x^{2.6}x-3.5=4.2x+1.2

解答

x^{2.6} x - 3.5 = 4.2 x + 1.2

解答

x = - 0.93332 \dots, x = 2.05298 \dots

求解步骤

x^{2.6} x - 3.5 = 4.2 x + 1.2

使用以下的指数特性

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

x^{2.6} = (x^{\frac{1}{5}})^{(2.6 \cdot 5)}

(x^{\frac{1}{5}})^{13} (x^{\frac{1}{5}})^{5} - 3.5 = 4.2 (x^{\frac{1}{5}})^{5} + 1.2

用

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

改写方程式

u^{13} u^{5} - 3.5 = 4.2 u^{5} + 1.2

解

u^{13} u^{5} - 3.5 = 4.2 u^{5} + 1.2 : u \approx - 0.98629 \dots, u \approx 1.15472 \dots

u \approx - 0.98629 \dots, u \approx 1.15472 \dots

代回

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

，求解

x

解

x^{\frac{1}{5}} = - 0.98629 \dots : x = - 0.93332 \dots

解

x^{\frac{1}{5}} = 1.15472 \dots : x = 2.05298 \dots

x = - 0.93332 \dots, x = 2.05298 \dots

验证解:

x = - 0.93332 \dots

真

, x = 2.05298 \dots

真

解为

x = - 0.93332 \dots, x = 2.05298 \dots

作图

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