Question

求帮忙做一下这个题吧

Answer 1

令x+y=u
y/x=v
解得x=u/（v+1）
y=uv/（v+1）
f（u,v）=f(x+y,y/x)=x²-y²=（x+y）（x-y）=u[u/（v+1）-uv/（v+1）]=-u²(1-v)/(v+1)
f(u,v)=-u²(1-v)/(v+1)
所以f(x,y)=x²(y-1)/(y+1)

Answer 2

答：
设x+y=t，y/x=s
则有：y=sx
所以：x+sx=t
解得：x=t /(1+s)
所以：y=st/(1+s)
代入条件式得：
f(x+y,y/x)=(x+y)(x-y)
f(t,s)=t(t-st)/(1+s)
=t²(1-s)/(1+s)
所以：
f(x,y)=x²(1-y)/(1+y)

Answer 3

x^2-y^2=(x+y)(x-y)=(x+y)^2(x-y)/(x+y)
而(x-y)/(x+y)=(1-y/x)/(1+y/x) 于是f(x,y)=x^2*(1-y)/(1+y)

Answer 4