十万火急~已知：x1＜x2＜x3,y1＜y2＜y3 x1+x2+x3=y1+y2+y3 x1x2+x2x3+x3x1=y1y2+y2y3+y3已知：x1＜x2＜x3,y1＜y2＜y3x1+x2+x3=y1+y2+y3x1x2+x2x3+x3x1=y1y2+y2y3+y3y1若x1＜y1求证；x2＞y2且x3小于y3我一点思路也没有,麻烦把过

Question

十万火急~已知：x1＜x2＜x3,y1＜y2＜y3 x1+x2+x3=y1+y2+y3 x1x2+x2x3+x3x1=y1y2+y2y3+y3
已知：x1＜x2＜x3,y1＜y2＜y3
x1+x2+x3=y1+y2+y3
x1x2+x2x3+x3x1=y1y2+y2y3+y3y1
若x1＜y1
求证；x2＞y2且x3小于y3
我一点思路也没有,麻烦把过程写得清楚一点,

Answer 1

构造函数f(x)=(x-x1)(x-x2)(x-x3)=x^3-(x1+x2+x3)x^2+(x1x2+x2x3+x3x1)x-x1x2x3,其图像与x轴交于三点（x1,0）,（x2,0),(x3,0)
g(x)=(x-y1)(x-y2)(x-y3)=x^3-(y1+y2+y3)x^2+(y1y2+y2y3+y3y1)x-y1y2y3,其图像与x轴交于三点（y1,0）,（y2,0),(y3,0)
因为x1+x2+x3=y1+y2+y3
x1x2+x2x3+x3x1=y1y2+y2y3+y3y1
且x1＜y1
所以只需将f(x)的图像向下平移就可得g(x)的图像,有图像知,x2＞y2且x3小于y3