Question

高数不懂了,f(x+y,y/x)=x2+y2,求（x,y）

Answer 1

令m=x+y,n=y/x,解得:

x=m/(n+1)；y=mn/(n+1)

代入f(x+y,y/x)=x2+y2得：

f(m,n)=(m/(n+1))^2+(mn/(n+1))^2=m^2(n^2+1)/(n+1)^2

所以,f(x,y)=x^2(y^2+1)/(x+1)^2