Đáp án:
$\\$
`a,`
`A = 9^2 |6x + 600|`
`↔ A = 81 |6x + 600|`
Vì $|6x + 600| \geqslant 0 ∀ x$
$↔ 81 |6x + 600| \geqslant 0$
$↔ A \geqslant 0$
`↔ min A = 0`
Dấu "`=`" xảy ra khi :
`↔ 6x + 600 = 0`
`↔ 6x = -600`
`↔ x = -100`
Vậy `min A = 0 ↔ x = -100`
$\\$
`b,`
`B = |x + 1236| + |x - 2744|`
`↔ B = |x + 1236| + |2744 - x|`
Áp dụng BĐT $|a| + |b| \geqslant |a + b|$
$↔ |x + 1236| + |2744 - x| \geqslant |x + 1236 + 2744 - x| = |3980| = 3980$
$↔ B \geqslant 3980$
`↔ min B = 3980`
Dấu "`=`" xảy ra khi :
$↔ (x + 1236) (2744 - x) \geqslant 0$
$↔$ \(\left[ \begin{array}{l}\left\{ \begin{array}{l}x+1236\geqslant 0 \\2744 - x \geqslant 0\end{array} \right.\\ \left\{ \begin{array}{l}x+1236 \leqslant0\\2744 - x\leqslant0 \end{array} \right.\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}\left\{ \begin{array}{l}x\geqslant -1236\\ x \leqslant 2744\end{array} \right.\\ \left\{ \begin{array}{l}x \leqslant -1236\\ x\geqslant 2744 \end{array} \right. \text{(Loại)}\end{array} \right.\)
$↔ -1236 \leqslant x \leqslant2744$
Vậy `min B = 3980` $↔ -1236 \leqslant x \leqslant 2744$
