Question

高等数学题

设f(x+y,x-y)=xy+y^2,则f(x,y)=

Answer 1

换元：x+y = u, x-y = v => x = (u+v)/2, y = (u-v)/2
f(u, v) = (u+v)/2 * (u-v)/2 + ((u-v)/2)^2 = 1/2 u (u - v)
即f(x,y) =1/2 x(x-y).