关于二次根式..
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/08/17 17:18:54
关于二次根式
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![](http://img.wesiedu.com/upload/a/6c/a6c8866c470765cd447553a16ab45e03.jpg)
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![](http://img.wesiedu.com/upload/a/6c/a6c8866c470765cd447553a16ab45e03.jpg)
![关于二次根式..](/uploads/image/z/15856875-27-5.jpg?t=%E5%85%B3%E4%BA%8E%E4%BA%8C%E6%AC%A1%E6%A0%B9%E5%BC%8F..)
1/(1+√2)
=(√2-1)/(√2+1)(√2-1)
=(√2-1)/(2-1)
=√2-1
1/(√2+√3)
=(√3-√2)/(√3-√2)(√3+√2)
=(√3-√2)/(3-2)
=√3-√2
后面以此类推
所以原式=√2-1+√3-√2+……+√9-√8
=√9-1
=2
=(√2-1)/(√2+1)(√2-1)
=(√2-1)/(2-1)
=√2-1
1/(√2+√3)
=(√3-√2)/(√3-√2)(√3+√2)
=(√3-√2)/(3-2)
=√3-√2
后面以此类推
所以原式=√2-1+√3-√2+……+√9-√8
=√9-1
=2