Question

二元函数问题,求f(x,y) 1.f(x+y,x-y)=2(x^2+y^2)e^(x^2-y^2) 2.f(x+y,xy)=2x^2+xy+2y^2

Answer 1

1.f(x+y,x-y)=2(x^2+y^2)e^(x^2-y^2)
令销慎x+y=m,x-y=n
则x=(m+n)/2,y=(m-n)/2
所以f(m,n)=2[(m+n)^2/4 + (m-n)^2/4] * e^[(m+n)^2/4 - (m-n)^2/4]
=(m^2+n^2) * e^(mn)
所以顷宏f(x,y）=(x^2+y^2) * e^(xy)
2.f(x+y,xy)=2x^2+xy+2y^2
=2(x^2+y^2)+xy
=2[(x+y)^2-2xy]+xy
=2(x+y)^2-3xy
所以亏乎敬f(x,y)=2x^2-3y