Question

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( )

Answer 1

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 ==>(y^2-ay-cy+ac)+(y^2-by)=0 ==>(y-a)(y-c)+y(y-b)=0 要等式为0,(y-a)(y-c),和y(y-b)应该是一个互为相反数,i) ∴{(y-a)(y-c)>0,y(y-b){y>a,y>c,y