Question

Tìm GTNN H=2x²+y²+2xy+6x+4y+9

Answer 1

H=2x²+y²+2xy+6x+4y+9

= (x²+2xy+y²)+(4x+4y)+4+(x²+2x+1)+4

= (x+y)²+4(x+y)+4 +(x+1)²+4

=(x+y+2)² +(x+1)²+4

=> MinH =4 khi x=-1; y=-1

Answer 2

H=2x²+y²+2xy+6x+4y+9

= (x²+2xy+y²)+(4x+4y)+4+(x²+2x+1)+4

= [(x+y)²+4(x+y)+4] +(x+1)²+4

=(x+y+2)² +(x+1)²+4

do (x+y+2)²≥0 ∀x;y

(x+1)² ≥0 ∀x

=> (x+y+2)² +(x+1)²+4 ≥4

=> min H= 4 khi x=-1;y=-1

Answer 3

H=2x2+y2+2xy+6x+4y+9

= (x2+2xy+y2)+(4x+4y)+4+(x2+2x+1)+4

= [(x+y)2+4(x+y)+4] +(x+1)2+4

=(x+y+2)2 +(x+1)2+4

Ta có: (x+y+2)2≥0 ∀x;y

(x+1)2 ≥0 ∀x

=> (x+y+2)2 +(x+1)2+4 ≥4

Vậy GTNN của H= 4 khi x=-1;y=-1