展开 (867(2+sqrt(3))sqrt(2-\sqrt{3)})/(1960)

解答

展开

\frac{867 ( 2 + 3 ) 2 - 3}{1960}

\frac{867 2 - 3}{980} + \frac{867 6 - 3 3}{1960}

十进制

0.85454 \dots

求解步骤

\frac{867 ( 2 + 3 ) 2 - 3}{1960}

乘开

867 (2 + 3) 2 - 3 : 1734 2 - 3 + 867 6 - 33

= \frac{1734 2 - 3 + 867 6 - 3 3}{1960}

使用分式法则:

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

\frac{1734 2 - 3 + 867 6 - 3 3}{1960} = \frac{1734 2 - 3}{1960} + \frac{867 6 - 3 3}{1960}

= \frac{1734 2 - 3}{1960} + \frac{867 6 - 3 3}{1960}

消掉

\frac{1734 2 - 3}{1960} : \frac{867 2 - 3}{980}

= \frac{867 2 - 3}{980} + \frac{867 6 - 3 3}{1960}

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