if
sqrt(x+1)-sqrt(x)
inequality
2007-06-19 11:55 pm
回答 (2)
2007-06-20 12:26 am
✔ 最佳答案
√x +√(x+1) > √x + √(x-1)1/{√x +√(x+1) } < 1/{ √x + √(x-1) }
[1/{√x +√(x+1) }] {√(x+1) - √x}/{√(x+1) - √x} < [1/{ √x +√(x-1) }] {√x -√(x-1)}/{√x -√(x-1)}
{√(x+1) - √x}/{ (x+1) - x} < {√x -√(x-1)}/{x -(x-1)}
{√(x+1) - √x}/{1} < {√x -√(x-1)}/{1}
√(x+1) - √x < √x -√(x-1)
2007-06-20 7:31 pm
sqrt(x+1) - sqrt(x) < sqrt(x) - sqrt(x-1)
1/[sqrt(x+1) + sqrt(x)] < 1/[sqrt(x) + sqrt(x-1)]
<-------left sign times [sqrt(x+1)+sqrt(x)]/[sqrt(x+1)+sqrt(x)]
<-------right sign times [sqrt(x)+sqrt(x-1)]/[sqrt(x)+sqrt(x-1)]
1/[sqrt(x+1) + sqrt(x)] < 1/[sqrt(x) + sqrt(x-1)]
<-------left sign times [sqrt(x+1)+sqrt(x)]/[sqrt(x+1)+sqrt(x)]
<-------right sign times [sqrt(x)+sqrt(x-1)]/[sqrt(x)+sqrt(x-1)]
參考: eat brain
收錄日期: 2021-04-12 21:43:40
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070619000051KK02555