展开 (pi(18*2^{2/3}-14))/(15)

解答

展开

\frac{π ( 18 \cdot 2 ^{\frac{2}{3}} - 14 )}{15}

\frac{6 \cdot 2 ^{\frac{2}{3}} π}{5} - \frac{14 π}{15}

十进制

3.05220 \dots

求解步骤

\frac{π ( 18 \cdot 2 ^{\frac{2}{3}} - 14 )}{15}

乘开

π (18 \cdot 2^{\frac{2}{3}} - 14) : 18 \cdot 2^{\frac{2}{3}} π - 14 π

= \frac{18 \cdot 2 ^{\frac{2}{3}} π - 14 π}{15}

使用分式法则:

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

\frac{18 \cdot 2 ^{\frac{2}{3}} π - 14 π}{15} = \frac{18 \cdot 2 ^{\frac{2}{3}} π}{15} - \frac{14 π}{15}

= \frac{18 \cdot 2 ^{\frac{2}{3}} π}{15} - \frac{14 π}{15}

消掉

\frac{18 \cdot 2 ^{\frac{2}{3}} π}{15} : \frac{6 \cdot 2 ^{\frac{2}{3}} π}{5}

= \frac{6 \cdot 2 ^{\frac{2}{3}} π}{5} - \frac{14 π}{15}

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