Question

已知a=√2012-√2011,b=√2013-√2012,c=√2014-√2013,比较a,b,c的大小

Answer 1

解答：
利用分子有理化
a=√2012-√2011
=(√2012-√2011)/1
=(√2012-√2011)*(√2012+√2011)/(√2012+√2011)
=(2012-2011)/(√2012+√2011)
=1/(√2012+√2011)
同样的方法
b=1/(√2013+√2012)
c=1/(√2014+√2013)
∵ 0<√2012+√2011<√2013+√2012<√2014+2013
∴ 1/(√2012+√2011)>1/(√2013+√2012)>1/(√2014+√2013)
即 a>b>c

Answer 2

a=√2012-√2011=1/(√2012+√2011)
b=√2013-√2012=1/(√2013+√2012)
c=√2014-√2013=1/(√2014+√2013)
因为√2014+√2013＞√2013+√2012＞√2012+√2011＞0
所以，a＞b＞c

Answer 3

a=√2012-√2011
a²＝1-2√2012*2011
b=√2013-√2012
b²＝1-2√2013*2012
c=√2014-√2013
c²＝1-2√2014*3013
∵√2014*3013＞√2013*2012＞√2012*2011
∴1-2√2014*3013＜1-2√2013*2012＜1-2√2012*2011
∴c²＜b²＜a²
∴a＞b＞c