$\text { Đáp án: }$
` A = x² + 2x + 3 `
` <=> A = (x² + 2x + 1) + 2 `
` <=> A = (x + 1)² + 2 `
$\text { Vì }$ ` (x + 1)² ≥ 0 ` ` ∀ ` ` x `
` => (x + 1)² + 2 ≥ 2 ` ` ∀ ` ` x `
$\text { Vậy }$ ` A_min = 2 ` $\text { dấu "=" xảy ra khi }$ ` x + 1 = 0 ` ` <=> ` ` x = –1 `
` B = x² – 4x + 5 `
` <=> B = (x² – 4x + 4) + 1 `
` <=> B = (x – 2)² + 1 `
$\text { Vì }$ ` (x – 2)² ≥ 0 ` ` ∀ ` ` x `
` => (x – 2)² + 1 ≥ 1 ` ` ∀ ` ` x `
$\text { Vậy }$ ` B_min = 1 ` $\text { dấu "=" xảy ra khi }$ ` x – 2 = 0 ` ` <=> ` ` x = 2 `