aa-2ab+bb≥0==>aa+bb≥2ab
a+b=1=>aa+bb+2ab=1==>aa+bb=1-2ab
1-2ab≥2ab
1≥4ab
1/a+1/b
=(a+b)/ab=1/ab
1/a+1/b≥4
(a+1/2)(b+1/2)=ab+1/2+1/4≤1（第一问结论）
√(a+1/2)(√b+1/2)≤1
(√a+1/2+√b+1/2)^2
=a+1/2+b+1/2+2√(a+1/2)(√b+1/2)
=2+2√(a+1/2)(√b+1/2)≤4
所以√a+1/2+√b+1/2≤2