Question

x,y∈R 且x^2+y^2/2=1 .求证:(X乘以根号1+y^2)的最大值

Answer 1

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