这题怎么做 求解
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∴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
∴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
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