Đáp án: 2010
Giải thích các bước giải:
Ta có:
A=5x2+2y2+4xy−2x+4y+19
→A=5x2+(4xy−2x)+2y2+4y+19
→A=5x2+2x(2y−1)+2y2+4y+19
→A=5(x2+2x⋅2y−15)+2y2+4y+19
→A=5(x2+2x⋅2y−15+(2y−15)2−(2y−15)2)+2y2+4y+19
→A=5(x2+2x⋅2y−15+(2y−15)2)−5⋅(2y−15)2+2y2+4y+19
→A=5(x+2y−15)2+6y2+24y−15+19
→A=5(x+2y−15)2+6(y2+4y)−15+19
→A=5(x+2y−15)2+6(y2+4y+4)−24−15+19
→A=5(x+2y−15)2+6(y+2)2−255+19
→A=5(x+2y−15)2+6(y+2)25−5+19
→A=5(x+2y−15)2+6(y+2)25+14
→A≥2010
Dấu = xảy ra khi {x+2y−15=0y+2=0
