函数f(xy,y^2/x)=x^2+y^2,求f(y^2/x,xy)

Question

函数f(xy,y^2/x)=x^2+y^2,求f(y^2/x,xy)

Answer 1

f(xy,y^2/x)=x^2+y^2
设xy=a
y^2/x=b
得
x=a^(2/3)b^(-1/3)
y=a^(1/3)b^(1/3)
得
f(a,b)=a^(2/3)b^(2/3)+a^(4/3)b^(-2/3)
所以
f(y^2/x,xy)=y^2+y^2/x^2