f(x+y,y/x)=x的平方+y的平方,求f(x,y)=?
热心网友
令t=x+y,u=y/x解得x=t/(1+u)y=ut/(1+u)所以f(t,u)=t^2/(1+u)^2+t^2*u^2/(1+u)^2=t^2(1+u^2)/(1+u)^2f(x,y)=x^2(1+y^2)/(1+y)^2
热心网友
设x+y=m,y/x=n,则x=m/(n+1),y=mn/(n+1),代入得:f(m,n)=[m^2+(mn)^2]/(n+1)^2将m换成x,n换成y得:f(x,y)=[x^2+(xy)^2]/(y+1)^2