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【比较大小:1.根号2005-根号2006与根号2006-根号2007】
题目内容:
比较大小:1.根号2005-根号2006与根号2006-根号2007优质解答
.√2005-√2006
=(√2005-√2006)/1
=(.√2005-√2006)(√2005+√2006)/(√2005+√2006)
=(2005-2006)/(√2005+√2006)
=-1/√(2005+2006)
同理√2006-√2007=-1/(√2006+√2007)
∵√ 2005+√2006<√2006+√2007
∴1/(√ 2005+√2006)>1/(√2006+√2007)
∴-1/(√ 2005+√2006)
优质解答
=(√2005-√2006)/1
=(.√2005-√2006)(√2005+√2006)/(√2005+√2006)
=(2005-2006)/(√2005+√2006)
=-1/√(2005+2006)
同理√2006-√2007=-1/(√2006+√2007)
∵√ 2005+√2006<√2006+√2007
∴1/(√ 2005+√2006)>1/(√2006+√2007)
∴-1/(√ 2005+√2006)
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