高数:f(x+y,x-y)=(x^2-y^2)⼀(x^2+y^2),则f(x,y)=

2025-05-22 17:31:27
推荐回答(1个)
回答1:

令 s = x+y ,t = x-y ,
则 x = (x+t)/2,y = (s-t)/2 ,且 s^2+t^2 = (x+y)^2+(x-y)^2 = 2(x^2+y^2) ,
所以 f(s,t) = f(x+y,x-y) = (x^2-y^2)/(x^2+y^2)
= st / [(s^2+t^2)/2]
= 2st / (s^2+t^2) ,
换用 x、y ,得 f(x,y) = 2xy / (x^2+y^2) 。