Question

已知f（x+y，x-y）=x^2-y^2+xy 求f(x,y)

只需最后答案，不求过程

Answer 1

u=x+y
v=x-y
x=(u+v)/2 , y=(u-v)/2,
f(u,v) = f（x+y，x-y）=x^2-y^2+xy =(u+v)^2/4+(u-v)^2/4 + (u+v)/2 *(u-v)/2
= (3u^2+v^2)/4

f(x,y)= (3x^2+y^2)/4

Answer 2

1/4(x^2)+xy-1/4(y^2)