A= 2x²+ y²+ 2xy- 8x+ 2028
= (x²+ 2xy+y²)+(x²-8x+ 16)+ 2012
= (x+y)²+ (x-4)²+ 2012 ≥ 2012
Dấu "=' xảy ra <=> x=-y= 4
Vậy minA= 2012 <=>x=-y= 4
B= |x-2026|+|x-2007|+2006
Áp dụng BĐT: |A|+ |B| ≥ |A-B| <=> AB ≤ 0
=> B ≥ |x-2026- x+ 2007|+ 2006 = 2025
Dấu "=" xảy ra <=> (x-2026)(x-2007) ≤ 0
<=> 2007 ≤ x ≤ 2026