若A=10061006/10071007B=10071007/10081008C=10081008/10091009,问A,B,C谁最大

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 07:29:10

若A=10061006/10071007B=10071007/10081008C=10081008/10091009,问A,B,C谁最大
若A=10061006/10071007
B=10071007/10081008
C=10081008/10091009,
问A,B,C谁最大

若A=10061006/10071007B=10071007/10081008C=10081008/10091009,问A,B,C谁最大
好!
1-A=1/10071007
1-B=1/10081008
1-C=1/10091009
∵1/10091009<1/10081008<1/10071007
∴C>B>A
C最大

A最小,C最大

B/A=(10071007/10081008)/(10061006/10071007)
=(10071007)^2/(10061006*10081008)
=(10071007)^2/[(1006*1008)*(1001)^2]
=(10071007)^2/[(1007-1)*(1007+1)*(1001)^2]
=(...

全部展开

B/A=(10071007/10081008)/(10061006/10071007)
=(10071007)^2/(10061006*10081008)
=(10071007)^2/[(1006*1008)*(1001)^2]
=(10071007)^2/[(1007-1)*(1007+1)*(1001)^2]
=(10071007)^2/[(1007^2-1)*(1001)^2]
=(10071007)^2/[(10071007^2-(1001)^2]>1
B>A
C/B=(10081008/10091009)/(10071007/10081008)
=(10081008)^2/(10071007*10091009)
=(10081008)^2/[(1007*1009)*(1001)^2]
=(10081008)^2/[(1008-1)*(1008+1)*(1001)^2]
=(10081008)^2/[(1008^2-1)*(1001)^2]
=(10081008)^2/[(10081008^2-(1001)^2]>1
C>B
C最大

收起

c最大