Giải:
a, `A = x^2 - x - 5`
`= x^2 - 2x . 1/2 + 1/4 - 21/4`
`= (x - 1/2)^2 - 21/4`
Vì `(x - 1/2)^2 ≥ 0` `(∀x)`
`-> (x - 1/2)^2 - 21/4 ≥ -21/4`
Dấu "=" xảy ra khi `(x - 1/2)^2 = 0`
`→ x - 1/2 = 0`
`→ x = 1/2`
Vậy `MIN_{A} = -21/4 ⇔ x = 1/2`
b, `B = x^2 - x`
`= x^2 - 2x . 1/2 + 1/4 - 1/4`
`= (x - 1/2)^2 - 1/4`
Vì `(x - 1/2)^2 ≥ 0` `(∀x)`
`-> (x - 1/2)^2 - 1/4 ≥ -1/4`
Dấu "=" xảy ra khi `(x - 1/2)^2 = 0`
`→ x - 1/2 = 0`
`→ x = 1/2`
Vậy `MIN_{B} = -1/4 ⇔ x = 1/2`
