设z=x+y+f(x-y),若当y=0时,z=x^2.求函数f及z
问题描述:
设z=x+y+f(x-y),若当y=0时,z=x^2.求函数f及z
答
当y=0时,z=x+f(x)=x^2,则f(x)=x^2-x.
则f(x-y)=(x-y)^2-(x-y)=x^2+y^2-2xy-x+y,
z=x+y+x^2+y^2-2xy-x+y=x^2+y^2-2xy+2y