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受欢迎的代数 >

x^{2.4}+2x^{1.2}-8=0

解答

x^{2.4} + 2 x^{1.2} - 8 = 0

解答

x = 2^{\frac{5}{6}}, x = - 2^{\frac{5}{6}}

+1

十进制

x = 1.78179 \dots, x = - 1.78179 \dots

求解步骤

x^{2.4} + 2 x^{1.2} - 8 = 0

使用以下的指数特性

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

x^{2.4} = (x^{\frac{1}{5}})^{(2.4 \cdot 5)}, x^{1.2} = (x^{\frac{1}{5}})^{(1.2 \cdot 5)}

(x^{\frac{1}{5}})^{12} + 2 (x^{\frac{1}{5}})^{6} - 8 = 0

用

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

改写方程式

u^{12} + 2 u^{6} - 8 = 0

解

u^{12} + 2 u^{6} - 8 = 0 : u = 32, u = - 32

u = 32, u = - 32

代回

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

，求解

x

解

x^{\frac{1}{5}} = 32 : x = 2^{\frac{5}{6}}

解

x^{\frac{1}{5}} = - 32 : x = - 2^{\frac{5}{6}}

x = 2^{\frac{5}{6}}, x = - 2^{\frac{5}{6}}

验证解:

x = 2^{\frac{5}{6}}

真

, x = - 2^{\frac{5}{6}}

真

解为

x = 2^{\frac{5}{6}}, x = - 2^{\frac{5}{6}}

作图

流行的例子

sqrt(y+3)=(y+3)/4

y + 3 = \frac{y + 3}{4}

2 x + 6 = x - 1

(x/(1-x))^{0.88}=0.312

(\frac{x}{1 - x})^{0.88} = 0.312

x=sqrt(2x+16)-8

x = 2 x + 16 - 8

(x/(1-x))^{0.88}=0.838

(\frac{x}{1 - x})^{0.88} = 0.838