设a>b>c>d>0,且x=√ab+√cd,y=√ac+√bd,z=√ad+√bc,

题目

设a>b>c>d>0,且x=√ab+√cd,y=√ac+√bd,z=√ad+√bc,
设a>b>c>d>0,且x=√ab+√cd,y=√ac+√bd,z=√ad+√bc,则x,y,z的大小关系为（ ）
A.x

答案

x-y=√ab+√cd-√ac-√bd
=(√ab-√ac)-(√bd-√cd)
=√a(√b-√c)-√d(√b-√c)
=(√a-√d)(√b-√c)>0
=>x>y
排除A,C
y-z=√ac+√bd-√ad-√bc
=(√ac-√ad)-(√bc-√bd)
=√a(√c-√d)-√b(√c-√d)
=(√a-√b)(√c-√d)>0
=>y>z
选D