Ai giúp em với ạ em cảm nhiều.

`a) 4x^2 + 4x + 3 `

`= 4x^2 + 4x + 1 + 2 `

`= ( 2x + 1 )^2 + 2 `

`o. ( 2x + 1 )^2 ≥ 0  ∀  x `

`<=> ( 2x + 1 )^2 + 2 ≥ 2  ∀  x`

Dấu"`=`" xảy ra `<=> ( 2x + 1 )^2 = 0`

                        ` <=> 2x + 1 = 0`

                        ` <=> x = - 1/2 `

Vậy GTNN là ` 2 ` khi ` x = - 1/2 `

`b) x^2 - x + 1 `

`= x^2 - 2x . 1/2 + 1/4 - 1/4 + 1 `

`= ( x - 1/2 )^2 + 3/4 `

`o. ( x - 1/2 )^2 ≥ 0 ∀ x `

`<=> ( x - 1/2 )^2 + 3/4 ≥ 3/4 ∀ x `

Dấu "`=`" xảy ra `<=> ( x - 1/2 )^2 = 0`

                          `<=> x - 1/2 = 0`

                          `<=> x = 1/2 `

Vậy GTNN là ` 3/4` khi ` x = 1/2 `

`c) x^2 + 5x + 7 `

`= x^2 + 2 . x . 5/2 + 25/4 - 25/4 + 7 `

`= ( x + 5/2 )^2 + 3/4 `

`o. ( x + 5/2 )^2 ≥ 0 ∀ x `

`<=> ( x + 5/2 )^2 + 3/4 ≥ 3/4 ∀ x` 

Dấu "`=`" xảy ra `<=> ( x + 5/2 )^2 = 0`

                         ` <=> x + 5/2 = 0`

                          `<=> x = - 5/2 `

Vậy GTNN là `3/4 ` khi ` x = - 5/2 `

`d) ( 2x - 1 ) ( x - 3 ) `

`= 2x^2 - 6x - x + 3 `

`= 2x^2 - 7x + 3 `

`= 2 ( x^2 - 7/2 x + 3/2 ) `

`= 2 ( x^2 - 2 . 7/4 + 49/16 - 49/16 + 3/2 ) `

`= 2 ( x - 7/4 )^2 - 25/8 `

`o. 2 ( x - 7/4 )^2 ≥ 0 ∀ x `

`<=> 2 ( x - 7/4 )^2 - 25/8 ≥ - 25/8 ∀ x `

Dấu "`=`" xảy ra `<=> ( x - 7/4 )^2 = 0 <=> x = 7/4 `

Vậy GTNN là `- 25/8 ` khi `x = 7/4`