已知x,y∈R,求证:x-xy+y≥x+y-1
问题描述：
已知x,y∈R,求证:x-xy+y≥x+y-1
答
证明：X^2-XY+Y^2>=X+Y-12X^2-2XY+2Y^2>=2Y+2X-2 两边同时乘以2(X-Y)^2+X^2-2X+1+Y^2-2Y+1>=0 移项凑完全平方项 (X-Y)^2+(X-1)^2+(Y-1)^2>=0
已知x,y∈R,求证:x-xy+y≥x+y-1
证明：X^2-XY+Y^2>=X+Y-12X^2-2XY+2Y^2>=2Y+2X-2 两边同时乘以2(X-Y)^2+X^2-2X+1+Y^2-2Y+1>=0 移项凑完全平方项 (X-Y)^2+(X-1)^2+(Y-1)^2>=0