Đáp án:
$A = x² - 6x - 5 $
$A = x² - 2.3x + 3² - 14 $
$A = (x - 3)² - 14 \geq - 14 $
$⇒Amin = -14 ⇔ (x - 3)² = 0 $
$⇔ x = 3 $
Vậy $Amin = - 14$ khi $x = 3 $
b,B = - x² - 8x +1 $
$B = - ( x² + 8x - 1) $
$B = - (x² + 2.4x + 16 - 17) $
$B = 17 - (x + 4)² \leq 17 $
$⇒ Bmax = 17 ⇔ (x + 4)² = 0 $
$⇔ x = - 4$
Vậy $Bmax = 17 $ khi $x = - 4$
$c,C = x² - x + 10 $
$C = x² - 2.\frac{1}{2}.x + \frac{1}{4} + \frac{39}{4} $
$C = (x - \frac{1}{2})² + \frac{39}{4 } \geq \frac{39}{4} $
$⇒ Cmin = \frac{39}{4} ⇔ (x - \frac{1}{2})² = 0 $
$⇔ x = \frac{1}{2} $
Vậy $Cmin = \frac{39}{4} $ khi $x = \frac{1}{2} $
