实数x、y满足x≥y≥1和2x^2-xy+5x-y+4=0,则x+y=___能写清楚就写清楚.
问题描述：
实数x、y满足x≥y≥1和2x^2-xy+5x-y+4=0,则x+y=___
能写清楚就写清楚.
答
2X^2 －XY－5X+Y+4
=X^2+X(X-Y)-4X-X+Y+4
=(X-2)^2+(X-1)(X-Y)=0
x≥y≥1
(x-2)^2>=0,x-1>=0,x-y>=0,即(x-1)(x-y)>=0
两项都非负,故均为0.
x-2=0,(x-1)(x-y)=0
即X=2 Y=2
X+Y=4