已知a>0,b>0,且h=min{a,b/(a²+b²)},求证：h≤√2/2
∵a,b＞0
a²+b²≥2ab--->a×b/(a²+b²)≤1/2
--->h = min{a,b/(a²+b²)}≤√(1/2) = √2/2