xl、x2是方程x2-2mx+（m2+2m+3）=O的两实根，则x12+x22的最小值是 ______．
方程有实根，则△=4m2-4（m2+2m+3）=-8m-12≥0，
故m≤-
，3 2
又有x1+x2=2m，x1•x2=m2+2m+3，
得x12+x22=（x1+x2）2-2x1•x2=2[（m-1）2-4]，
但m≤-
，3 2
故当m≤-
时，x12+x22的最小值为2[（-3 2
-1）2-4]=2×3 2
=9 4
．9 2
故答案为：
．9 2
| 完形填空。 | |||
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