这题怎么做 求解
答案:1 悬赏:30 手机版
解决时间 2021-11-23 21:00
- 提问者网友：眉目添风霜
- 2021-11-23 08:31
这题怎么做 求解
最佳答案
- 五星知识达人网友：零点过十分
- 2021-11-23 10:06
∴a+b=1⩾2ab−−√，
∴ab⩽14
∴(a+12−−−−−√+b+12−−−−−√)2=a+12+b+12+2a+12−−−−−√⋅b+12−−−−−√
=2+2ab+12(a+b)+14−−−−−−−−−−−−−−−√=2+2ab+34−−−−−−√⩽2+214+34−−−−−√=4，
∴(a+12−−−−−√+b+12−−−−−√)2⩽4
∴a+12−−−−−√+b+12−−−−−√的最大值是2追答
∴ab⩽14
∴(a+12−−−−−√+b+12−−−−−√)2=a+12+b+12+2a+12−−−−−√⋅b+12−−−−−√
=2+2ab+12(a+b)+14−−−−−−−−−−−−−−−√=2+2ab+34−−−−−−√⩽2+214+34−−−−−√=4，
∴(a+12−−−−−√+b+12−−−−−√)2⩽4
∴a+12−−−−−√+b+12−−−−−√的最大值是2追答
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