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受欢迎的代数 >

1.2x=8x^{0.12}

解答

1.2 x = 8 x^{0.12}

解答

x = 0, x = - 8.63495 \dots, x = 8.63495 \dots

求解步骤

1.2 x = 8 x^{0.12}

使用以下的指数特性

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

x^{0.12} = (x^{\frac{1}{25}})^{(0.12 \cdot 25)}

1.2 (x^{\frac{1}{25}})^{25} = 8 (x^{\frac{1}{25}})^{3}

用

x^{\frac{1}{25}} = u

改写方程式

1.2 u^{25} = 8 u^{3}

解

1.2 u^{25} = 8 u^{3} : u = 0, u = - 1.09005 \dots, u = 1.09005 \dots

u = 0, u = - 1.09005 \dots, u = 1.09005 \dots

代回

u = x^{\frac{1}{25}}

，求解

x

解

x^{\frac{1}{25}} = 0 : x = 0

解

x^{\frac{1}{25}} = - 1.09005 \dots : x = - 8.63495 \dots

解

x^{\frac{1}{25}} = 1.09005 \dots : x = 8.63495 \dots

x = 0, x = - 8.63495 \dots, x = 8.63495 \dots

验证解:

x = 0

真

, x = - 8.63495 \dots

真

, x = 8.63495 \dots

真

解为

x = 0, x = - 8.63495 \dots, x = 8.63495 \dots

作图

流行的例子

2=sqrt(3u-12)-1

2 = 3 u - 12 - 1

solvefor x,y^2=sqrt(x-1)

so l v e f or x, y^{2} = x - 1

0.2x^{1/3}=0.062x

0.2 x^{\frac{1}{3}} = 0.062 x

solvefor x,f^{-1}(x)=sqrt(2x)

so l v e f or x, f^{- 1} (x) = 2 x

sqrt(x)+sqrt(x-12)=2

x + x - 12 = 2