已知f(x+y,y/x)＝x^2-y^2,则f(x,y)＝多少已知f(x+y,y/x)＝x^2-y^2,则f(x,y)＝多少?懂的话教一下哈,

Question

已知f(x+y,y/x)＝x^2-y^2,则f(x,y)＝多少
已知f(x+y,y/x)＝x^2-y^2,则f(x,y)＝多少?懂的话教一下哈,

Answer 1

令 x+y=t y/x=k
∴y=kx
(1+k)x=t
x=t/(1+k)
y=kt/(1+k)
∴x²-y²=(x+y)(x-y)=t(t-kt)/(1+k)=t²(1-k)/(1+k)
f(t,k)=t²(1-k)/(1+k)
把t.y 用x,y代回,得
f(x,y)=x²(1-y)/(1+y)