( 2 4 4) ( 2 2 1) ( 2 2) 2007M = X + X+ + Y + Y+ + XY X− − Y+ + ( 2) (2 1) (2 2) ( 1) 2007M = −X + −Y + −X Y− + ( 2) 12( 1) 2 34( 1)2 2007⇒ = − + −  + − + M  X Y  YDO (Y−1)2 ≥0 VÀ (X− +2) 12(Y−1)2 ≥0  ∀X Y, 2007⇒M ≥ ⇒MMIN =2007⇔ =X 2;Y=1...

bài 2. - DE THI CHUYEN bài 2. - DE THI CHUYEN
Lớp 10 DE THI CHUYEN

Bài 2. Ta có :

(

2

4 4

) (

2

2 1

) (

2 2

)

2007M = x + x+ + y + y+ + xy x− − y+ +

(

2

) (

2

1

) (

2

2

) (

1

)

2007M = −x + −y + −x y− +

(

2

)

12

(

1

)

2

34

(

1

)

2

2007⇒ = − + −  + − +

Mx yy

Do (

y−1

)

2

≥0

và

(

x− +2

)

12

(

y−1

)

2

≥0  ∀x y,

2007⇒M ≥

⇒M

min

=2007⇔ =x 2;y=1

 = +1u x x = +