x^2+(y^2/2)=1x^2+(y^2+1)/2=1+1/21+1/2=3/2=x^2+(y^2+1)/2≥2x√[(y^2+1)/2]=√2*x*根号(1+y^2)所以x*根号(1+y^2)最大值为3√2/4