设0,＜a＜b＜c,实数x,y(x＞y)满足2x+2y=a+b+c,2xy=ac,则x,y的取值范围是( )

题目

设0,＜a＜b＜c,实数x,y(x＞y)满足2x+2y=a+b+c,2xy=ac,则x,y的取值范围是( )
A.a＜x＜b,0＜y＜a B.b＜x＜c,0＜y＜a
C.a＜x＜c,0＜y＜a D.b＜x＜c,a＜y＜c

答案

2x+2y=a+b+c ==>x=(a+b+c-2y)/2----------------------------------(1) 2xy=ac==>x=ac/2y-----------------------------------(2) (1)代入（2）得：ac/2y=(a+b+c-2y)/2 ==>ac=(a+b+c-2y)y ==>2y^2-ay-by-cy+ac=0 ==>...