Question

求多项式p=2a^2-8ab+17b^2-16a-4b+2059的最小值,并求p是最小值时,a与b的值

Answer 1

p=2a^2-8ab+17b^2-16a-4b+2059

=(a-4b)^2+(a-8)^2+(b-2)^2+2059-64-4

=(a-4b)^2+(a-8)^2+(b-2)^2+1991

p=0+0+0+1991

=1991

a=4b

b=2

a=8