展开 (12(sqrt(2)-e^{pi/(12)}))/(pie^{pi/4)}

解答

展开

\frac{12 ( 2 - e ^{\frac{π}{12}} )}{π e ^{\frac{π}{4}}}

\frac{12 2}{π e ^{\frac{π}{4}}} - \frac{12}{π e ^{\frac{π}{6}}}

十进制

0.20018 \dots

求解步骤

\frac{12 ( 2 - e ^{\frac{π}{12}} )}{π e ^{\frac{π}{4}}}

乘开

12 (2 - e^{\frac{π}{12}}) : 122 - 12 e^{\frac{π}{12}}

= \frac{12 2 - 12 e ^{\frac{π}{12}}}{π e ^{\frac{π}{4}}}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{12 2 - 12 e ^{\frac{π}{12}}}{π e ^{\frac{π}{4}}} = \frac{12 2}{π e ^{\frac{π}{4}}} - \frac{12 e ^{\frac{π}{12}}}{π e ^{\frac{π}{4}}}

= \frac{12 2}{π e ^{\frac{π}{4}}} - \frac{12 e ^{\frac{π}{12}}}{π e ^{\frac{π}{4}}}

消掉

\frac{12 e ^{\frac{π}{12}}}{π e ^{\frac{π}{4}}} : \frac{12}{π e ^{\frac{π}{6}}}

= \frac{12 2}{π e ^{\frac{π}{4}}} - \frac{12}{π e ^{\frac{π}{6}}}

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