设f(x+y,y/x)=x^2+y^2,则f(x,y)=?,f(x-y,xy)=?

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设f(x+y,y/x)=x^2+y^2,则f(x,y)=?,f(x-y,xy)=?设f(x+y,y/x)=x^2+y^2,则f(x,y)=?,f(x-y,xy)=?设f(x+y,y/x)=x^2+y^

设f(x+y,y/x)=x^2+y^2,则f(x,y)=?,f(x-y,xy)=?
设f(x+y,y/x)=x^2+y^2,则f(x,y)=?,f(x-y,xy)=?

设f(x+y,y/x)=x^2+y^2,则f(x,y)=?,f(x-y,xy)=?
设x+y=a,y/x=b,则有x=a/(b+1),y=ab/(b+1),故
f(x+y,y/x)=f(a,b)=x^2+y^2=[a/(b+1)]^2+[ab/(b+1)]^2=a^2(b^2+1)/(b+1)^2
即f(x,y)=x^2(y^2+1)/(y+1)^2
代入x-y和xy即得f(x-y,xy)

设X+Y=A,Y/X=B ==>X=A/(B+1),Y=BA/(B+1)
F(A,B)=(A/(B+1))^2+(BA/(B+1))^2
=(A^2+(BA)^2)/((B+1)^2)
所以F(X,Y)=(X^2+(YX)^2)/((Y+1)^2)
F(X-Y,XY)=((X-Y)^2+((X-Y)XY)^2)/((XY+1)^2)

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