Tìm GTNN của B = xy(x – 2)(y + 6) + 12x2

B = xy(x – 2)(y + 6) + 12x2 – 24x + 3y2 + 18y + 2045

B = xy(x – 2)(y + 6) + 12x2 – 24x + 3y2 + 18y + 2045

 

B = (x2 – 2x)(y2 + 6y) + 12(x2 – 2x) + 3(y2 + 6y) + 2045

B = (x2 – 2x + 3)(y2 + 6y + 12) + 2009

B = [(x – 1)2 + 2][(y + 2)2 + 3] + 2009

≥ 2.3 + 2009  = 2015

Vậy min B = 2015 khi x = 1; y = -2.