Question

已知函数f(x-y,y/x)=x^2-y^2,求f(x,y)

Answer 1

令a=x-y

b=x/y

则x=by

a=by-y

y=a/(b-1)

x=ab/(b-1)

则x+y=a(b+1)/(b-1)

所以x²-y²=a²(b+1)/(b-1)

f(a,b)=a²(b+1)/(b-1)

f(x,y)=x²(y+1)/(y-1)