Question

若x>1 则x加x-1分之9的最小值是?

若x<3 则x加x-3分之4的最大值是 (过程谢谢)

Answer 1

你好!
(1)
∵x>1
,x-1>0
x
+
9/(x-1)
=(x-1)
+
9/(x-1)
+1
≥2√[(x-1)*9/(x-1)]
+1
=7
当且仅当x-1=9/(x-1)即x=4时取等号
即x
+
9/(x-1)最小值是7.
(2)
∵x<3,
x-3<0
,3-x>0
x+
4/(x-3)
=
-[(3-x)
+
4/(3-x)
]
+3
≤
-
2√[(3-x)
*4/(3-x)]
+3
=
-1
当且仅当(3-x)
=4/(3-x)即x=
1时取等号
原式最大值为
-1.