Question

实数x、y满足x≥y≥1和2x^2-xy+5x-y+4=0,则x+y=___

Answer 1

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