设f(x+y,x-y)=xy+y2,求f(x,y)

hiigo,来这里提问的当然是有不清楚的地方,你厉害能否低调些?

s=x+y,t=x-y
x=(s+t)/2,y=(s-t)/2

f(x+y,x-y)=xy+y^2=y(x+y)=[(s-t)/2]*s
f(s,t)=(s^2-st)/2
f(x,y)=(x^2-xy)/2

s=x+y,t=x-y
x=(s+t)/2,y=(s-t)/2

f(x+y,x-y)=xy+y^2=y(x+y)=[(s-t)/2]*s
f(s,t)=(s^2-st)/2
f(x,y)=(x^2-xy)/2

a=x+y,b=x-y 则x=(a+b)/2 , y=(a-b)/2
f(a,b)=(a2-b2)/4+(a2-2ab+b2)/4=(a2-ab)/2
f(x,y)=(x2-xy)/2

s=x+y,t=x-y
x=(s+t)/2,y=(s-t)/2

f(x+y,x-y)=xy+y^2=y(x+y)=[(s-t)/2]*s
f(s,t)=(s^2-st)/2
f(x,y)=(x^2-xy)/2

设a=x+y,b=x-y所以x=1/2(a+b) y=1/2(a-b)
所以f(a,b)=1/4(a*a-b*b)+1/4(a*a-2ab+b*b)=1/2a*a-1/2ab
所以f(x,y)=1/2x*x-1/2xy