法一：∵a^2+1/4b^2=1∴a^2=1-1/4b^2,y=a√（1+b^2）=√[a^2(1+b^2)]=√[(1-1/4b^2)*(1+b^2)]=√[-1/4b^4+3/4b^2+1]=√[-1/4*（b^2-3/2)^2+25/16]∴当b^2=3/2时,a^2=5/8即b=√6/4,a=√10/4,y取最大值,ymax=5/4法二：...