设x、y、z均为正实数,且满足 z+2x+2yx+y<x+2y+2zy+z<y+2x+2zz+x,则x、y、z三个数的大小关系是______

2025-05-22 02:11:43
推荐回答(1个)
回答1:

z+2x+2y
x+y
x+2y+2z
y+z
y+2x+2z
z+x

z
x+y
+2<
x
y+z
+2<
y
z+x
+2

z
x+y
x
y+z
y
z+x
x+y
z
y+z
x
z+x
y
x+y
z
+1>
y+z
x
+1>
z+x
y
+1

x+y+z
z
y+z+x
x
z+x+y
y

∴z<x<y
故答案为:z<x<y.