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51问答网 > 根号2加上2的根号怎么化简这个是简写的，完整题目根号里面有好多根号2

根号2加上2的根号怎么化简这个是简写的，完整题目根号里面有好多根号2

2025-03-16 16:42:04

推荐回答（1个）

回答1：

令√[2+√(2+√2-------+√2)]=A
则有：A=√（2+A）
A²=A+2
A²-A-2=0
（A-2）（A+1）=0
A1=2
A2=-1（不合，舍去）
所以，√[2+√(2+√2-------+√2)]=2

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