f(x+y,y/x)=x^2-y^2

题目

f(x+y,y/x)=x^2-y^2
求f(x,y)

答案

令x+y=t,y/x=u则y=xu代入x+y=t,得x+xu=t(1) u≠-1,即y≠-x,t≠0时,x=t/(1+u)y=xu=ut/(1+u)∴f(t,u)=f(x+y,y/x)=x^2-y^2=[t/(1+u)]^2-[ut/(1+u)]^2=t^2(1-u^2)/(1+u)^2=t^2(1-u)/(1+u) （t≠0,u≠-1）∴f(x,y)=x^2(1-...