设f(x-y,y/x)=xy,则f(xy,x+y)等于什么

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设f(x-y,y/x)=xy,则f(xy,x+y)等于什么

设f(x-y,y/x)=xy,则f(xy,x+y)等于什么
设f(x-y,y/x)=xy,则f(xy,x+y)等于什么

设f(x-y,y/x)=xy,则f(xy,x+y)等于什么

设a-b=xy(1),b/a=x+y(2)
联合等式(1)、(2)可得:a=xy/(1-x-y),b=(x²y+xy²)/(1-x-y)
由题意可知f(x-y,y/x)=xy,则有f(a-b,b/a)=ab={xy/(1-x-y)}*{(x²y+xy²)/(1-x-y)}
=(x³y²+x²y³)/(1-x-y)
因为a-b=xy,b/a=x+y,则f(xy,x+y)=f(a-b,b/a)=(x³y²+x²y³)/(1-x-y)
答案:f(xy,x+y)=(x³y²+x²y³)/(1-x-y)