已知f(x+y,x-y)=x^2+3y^2,求f(x,y)

Question

如题所述

Answer 1

令x+y=s,x-y=t
x=(s+t)/2
y=(s-t)/2
f(s,t)=[(s+t)/2]^2+3[(s-t)/2]^2
=1/4 [4s²-4st+4t²]
=s²-st+t²
所以
f(x,y)=x²-xy+y²