已知实数x1、x2满足x12-6x1+2=0和x22-6x2+2=0,则x2x1+x1x2的值等于_.

问题描述:

已知实数x1、x2满足x12-6x1+2=0和x22-6x2+2=0,则

x2
x1
+
x1
x2
的值等于______.

∵方程x2-6x+2=0的两根之积为2,两根之和为6,

x2
x1
+
x1
x2
=
x 21
+
x 22
x1x2
=
(x1 +x2 )22x1x2
x1x2
=
62−2×2
2
=16.
故答案为16.