5A²+2B²-4AB-12A+46/3
=2A²-4AB+2B²+3A²-12A+46/3
=2(A²-2AB+B²)+3A²-12A+12+10/3
=2(A-B)²+3(A²-4A+4)+10/3
=2(A-B)²+3(A-2)²+10/3
因为(A-B)²≥0
(A-2)²≥0
所以2(A-B)²+3(A-2)²≥0
当2(A-B)²+3(A-2)²=0时,代数式有最小值,即A=B=2时,代数式有最小值
所以5A²+2B²-4AB-12A+46/3的最小值是10/3