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
的值等于______. x1 x2
答
∵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 )2−2x1x2
x1x2
=16.
62−2×2 2
故答案为16.