展开 (2(5+2*5^{1/2}))/5

解答

展开

\frac{2 ( 5 + 2 \cdot 5 ^{\frac{1}{2}} )}{5}

2 + \frac{4}{5 ^{\frac{1}{2}}}

十进制

3.78885 \dots

求解步骤

\frac{2 ( 5 + 2 \cdot 5 ^{\frac{1}{2}} )}{5}

乘开

2 (5 + 2 \cdot 5^{\frac{1}{2}}) : 10 + 4 \cdot 5^{\frac{1}{2}}

= \frac{10 + 4 \cdot 5 ^{\frac{1}{2}}}{5}

使用分式法则:

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

\frac{10 + 4 \cdot 5 ^{\frac{1}{2}}}{5} = \frac{10}{5} + \frac{4 \cdot 5 ^{\frac{1}{2}}}{5}

= \frac{10}{5} + \frac{4 \cdot 5 ^{\frac{1}{2}}}{5}

数字相除:

\frac{10}{5} = 2

= 2 + \frac{4 \cdot 5 ^{\frac{1}{2}}}{5}

消掉

\frac{4 \cdot 5 ^{\frac{1}{2}}}{5} : \frac{4}{5 ^{\frac{1}{2}}}

= 2 + \frac{4}{5 ^{\frac{1}{2}}}

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