已知a,b是方程x平方-2mx+m+6=0的兩個(gè)實(shí)數(shù)根,
由根與系數(shù)的關(guān)系得a+b=2m ab=m+6
(a-1)²+(b-1)²
=a²-2a+1+b²-2b+1
=(a+b)²-2(a+b)-2ab+2
=4m²-4m-2m-12+2
=4m²-6m-10
=4(m²-3/2m+9/16-9/16)-10
=4(m-3/4)²-49/4
△=4m²-4(m+6)
=4m²-4m-24≥0
m≤-2或 m ≥3
當(dāng)m=3時(shí)有最小值為4×（3-3/4)²-49/4=8