Question

设f(xy,x-y)=x²+y²,则f(x,y)=?

Answer 1

f(xy,x-y)=x²+y²=-2xy+(x-y)^2

因此f(x,y)=-2x+y^2

f(x-y,x+y)=xy=1/4[(x+y)+(x-y)][(x+y)-(x-y)]

f(x,y)=1/4(y+x)(y-x)=1/4(y^2-x^2)