(2X + 1) X2 −X+1 > (2X - 1) X2+X+1 (*) [(2X + 1) X2 −X+1]2 = 4X4 + X2 +3X +1

2. - DAP AN NAM DINH09 10
Toán DAP AN NAM DINH09 10

2. (2x + 1)

x

2

−x+1

> (2x - 1)

x

2

+x+1

(*)

[(2x + 1)

x

2

−x+1

]

2

= 4x

4

+ x

2

+3x +1.

[(2x - 1)

x

2

+x+1

]

2

= 4x

4

+ x

2

-3x + 1.

− 1 => VT < 0, VP < 0

+ Nếu x <

2

(*) ⇔ [(2x + 1)

x

2

−x+1

]

2

< [(2x - 1)

x

2

+x+1

]

2

⇔ 4x

4

+ x

2

+3x +1 < 4x

4

+ x

2

-3x + 1 ⇔ 3x < -3x (đúng)

1 ≤ x ≤

1 => VT ≥ 0, VP < 0 => (*) luôn đúng.

+ Nếu -

+ Nếu x ≥ 2 1 => VT > 0, VP > 0

=> (*) ⇔ [(2x + 1)

x

2

−x+1

]

2

> [(2x - 1)

x

2

+x+1

]

2

⇔ 4x

4

+ x

2

+3x +1 > 4x

4

+ x

2

-3x + 1 ⇔ 3x > -3x (đúng).

Vậy (*) luôn đúng với mọi x.