f(x+y,x-2y)=xx+yy，则f(x,y)=

更新时间2022-03-26 09:37:49

（1°）f(x+y，x-2y)=x²+y²

设 x+y=p①  x-2y=q②

①-②  3y=p-q  y=(p-q)/3③

①-③  x=p-(p-q)/3=(2p+q)/3④

代入1°

 f(p，q)=(2p+q)²/3²+(p-q)²/3²

=(5p²+2pq+2q²)/9

∴ f(x，y)=(5x²+2xy+2y²)/9