Question

题：设f（x+y,x-y）=xy+y^2,则f(x,y)=______(那是y的平方)

Answer 1

设x+y=a,x-y=b.则x=(a+b)/2,y=(a-b)/2

∵f(x+y,x-y)=xy+y²

∴f(a,b)=[(a+b)/2][(a-b)/2]+[(a-b)/2]²

=[(a-b)/2][(a+b)/2+(a-b)/2]

=a(a-b)/2

故f(x,y)=x(x-y)/2