z=x*(1+y^2)^0.5
z^2=x^2 *(1+y^2)
x^2=1-y^2/2
z^2=(1-y^2/2)*(1+y^2)
a=y^2
z^2=(1-a/2)*(1+a)=-a^2/2 +a/2 +1
a=1/2 z^2(max)=9/8
z(max)=(9/8)^0.5
在这最大值就为根号9/8