已知x、y、z均为正数，求证：33(1/x+1/y+1/z)≤1/x2+1/y2+1/z2．
问题描述：
已知x、y、z均为正数，求证：
(
3
3
+1 x
+1 y
)≤1 z
．
+1 x2
+1 y2
1 z2
答
证明：由柯西不等式得(12+12+12)(
+1 x2
+1 y2
)≥(1 z2
+1 x
+1 y
)2…（5分）1 z
则
×
3
≥
+1 x2
+1 y2
1 z2
+1 x
+1 y
，1 z
即
(
3
3
+1 x
+1 y
)≤1 z
…（10分）
+1 x2
+1 y2
1 z2