a²+b²/2=1 ,2a²+b²=2
a√(1+b²) =√[a² (1+b²)]=√1/2[2a² (1+b²)]
=√2/2•√[2a² (1+b²)]
≤√2/2•[(2a²+ (1+b²))/2]
=√2/2•(3/2)= 3√2/4.(2a² =1+b²时取到等号)