已知 x1,x2是方程x^2-2ax+a+6=0的两个实根，求（x1-1）^2+(x2-1)^2的最小值

有两个跟
则4a^2-4a-24>=0
a^2-a-6>=0
(a-3)(a+2)>=0
a>=3,a<=-2

x1+x2=2a,x1*x2=a-6
(x1+x2)^2=4a^2
x1^2+x2^2+2x1x2=4a^2
x1^2+x2^2=4a^2-2a+12

（x1-1）^2+(x2-1)^2
=(x1^2+x2^2)+1-(x1+x2)
=4a^2-2a+12+1-2a
=4a^2-4a+13
=4(a-1/2)^2+12
a>=3,a<=-2

所以a=3和a=-2时，最小值=37

有两个跟
则4a^2-4a-24>=0
a^2-a-6>=0
(a-3)(a+2)>=0
a>=3,a<=-2
x1+x2=2a,x1*x2=a-6
(x1+x2)^2=4a^2
x1^2+x2^2+2x1x2=4a^2
x1^2+x2^2=4a^2-2a+12
（x1-1）^2+(x2-1)^2
=(x1^2+x2^2)+1-(x1+x2)
=4a^2-2a+12+1-2a
=4a^2-4a+13
=4(a-1/2)^2+12
a>=3,a<=-2
所以a=3和a=-2时，最小值=37

有两个根
则4a^2-4a-24>=0
a^2-a-6>=0
(a-3)(a+2)>=0
a>=3,a<=-2

x1+x2=2a,x1*x2=a-6
(x1+x2)^2=4a^2
x1^2+x2^2+2x1x2=4a^2
x1^2+x2^2=4a^2-2a+12

（x1-1）^2+(x2-1)^2
=(x1^2+x2^2)+1-(x1+x2)
=4a^2-2a+12+1-2a
=4a^2-4a+13
=4(a-1/2)^2+12
a>=3,a<=-2

所以a=3和a=-2时，最小值=37

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