Question

设f(x+y,y/x)=x^2-y^2,求f(x-y,xy)

Answer 1

令x+y=u,y/x=v，则x=u/(1+v)，y=uv/(1+v)，故f(u,v)=u^2(1-v)/(1+v)，令u=x-y,v=xy，则f(x-y,xy)=(x-y)^2*(1-xy)/(1+xy)

Answer 2

您好，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)

Answer 3

解：设 x+y=t y/x=k
则y=kx
(1+k)x=t
x=t/(1+k)
y=kt/(1+k)
将x、y值带入方程中
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)