tim gia tri cua bieu thuc sau A=x^2+2x+5 b= x^2-x-51 27/11/2021 Bởi Josephine tim gia tri cua bieu thuc sau A=x^2+2x+5 b= x^2-x-51
Đáp án: $A = x² + 2x + 5 $ $A = x² + 2x + 1 + 4 $ $A = (x + 1)² + 4 \geq 4 ∀ x $ $⇒ Amin = 4 ⇔ (x + 1)² = 0 $ $ ⇔ x = – 1 $ $B = x² – x – 51 $ $B = x² – 2.\frac{1}{2}x + \frac{1}{4} – \frac{205}{4} $ $B = (x – \frac{1}{2})² – \frac{205}{4} \geq – \frac{205}{4}$ $⇒ Bmin = – \frac{205}{4} ⇔ x = \frac{1}{2} $ Bình luận
Đáp án:
$A = x² + 2x + 5 $
$A = x² + 2x + 1 + 4 $
$A = (x + 1)² + 4 \geq 4 ∀ x $
$⇒ Amin = 4 ⇔ (x + 1)² = 0 $
$ ⇔ x = – 1 $
$B = x² – x – 51 $
$B = x² – 2.\frac{1}{2}x + \frac{1}{4} – \frac{205}{4} $
$B = (x – \frac{1}{2})² – \frac{205}{4} \geq – \frac{205}{4}$
$⇒ Bmin = – \frac{205}{4} ⇔ x = \frac{1}{2} $