实数x1,x2满足x1^2-6(x1)+2=0和x2^2-6(x2)+2=0,求x2/x1+x1/x2
问题描述:
实数x1,x2满足x1^2-6(x1)+2=0和x2^2-6(x2)+2=0,求x2/x1+x1/x2
答
实数x1,x2满足x1^2-6(x1)+2=0和x2^2-6(x2)+2=0,
则,x1,x2是方程x^2-6x+2=0的两个根
所以,x1+x2=6,x1x2=2
x2/x1+x1/x2
=(x2^2+x1^2)/x1x2
=[(x1+x2)^2-2x1x2]/x1x2
=(x1+x2)^2/x1x2-2
=36/2-2
=18-2
=16