x,y为实数,证明x*2-xy+y*2>=x+y-1

问题描述:

x,y为实数,证明x*2-xy+y*2>=x+y-1

〔(x^2-xy+y^2)-(x+y-1)〕
=(x^2-2x+1)+(y^2-2y+1)+(x^2-2xy+y^2)
=(x-1)^2+(y-1)^2+(x-y)^2>=0