设a+b=2,b>0,则
|
∵a+b=2,∴
=1,a+b 2
∴
+1 2|a|
=|a| b
+a 4|a|
+b 4|a|
,|a| b
∵b>0,|a|>0,∴
+b 4|a|
≥1(当且仅当b2=4a2时取等号),|a| b
∴
+1 2|a|
≥|a| b
+1,a 4|a|
故当a<0时,
+1 2|a|
的最小值为|a| b
.3 4
故答案为:
.3 4
设a+b=2,b>0,则
|
∵a+b=2,∴
=1,a+b 2
∴
+1 2|a|
=|a| b
+a 4|a|
+b 4|a|
,|a| b
∵b>0,|a|>0,∴
+b 4|a|
≥1(当且仅当b2=4a2时取等号),|a| b
∴
+1 2|a|
≥|a| b
+1,a 4|a|
故当a<0时,
+1 2|a|
的最小值为|a| b
.3 4
故答案为:
.3 4