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受欢迎的代数 >

((x-1)/x)^{0.5}+((1-1)/x)^{0.5}=x

解答

(\frac{x - 1}{x})^{0.5} + (\frac{1 - 1}{x})^{0.5} = x

解答

x \in R 无解

求解步骤

(\frac{x - 1}{x})^{0.5} + (\frac{1 - 1}{x})^{0.5} = x

因式分解

(\frac{x - 1}{x})^{\frac{1}{2}} + (\frac{1 - 1}{x})^{\frac{1}{2}} : (\frac{x - 1}{x})^{\frac{1}{2}}

(\frac{x - 1}{x})^{\frac{1}{2}} = x

两边进行平方:

\frac{x - 1}{x} = x^{2}

\frac{x - 1}{x} = x^{2}

解

\frac{x - 1}{x} = x^{2} : x \approx - 1.32471 \dots

x \approx - 1.32471 \dots

验证解:

x \approx - 1.32471 \dots

假

解是

x \in R 无解

作图

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\frac{72}{( x ^{\frac{8}{5}} )} = \frac{( x ^{\frac{7}{5}} )}{24}

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