mng ơi giúp mik vs ak

Đáp án:

$a)\min_A=\dfrac{2019}{2020}\Leftrightarrow x=-\dfrac{3}{5}\\ b)\max_B=-4\Leftrightarrow x=\dfrac{2}{5}.$

Giải thích các bước giải:

$a) A=\dfrac{2019}{2020}+\left|-\dfrac{3}{5}-x\right|$

Do $\left|-\dfrac{3}{5}-x\right| \ge 0 \ \forall \ x$

$\Rightarrow \left|-\dfrac{3}{5}-x\right| +\dfrac{2019}{2020} \ge \dfrac{2019}{2020} \ \forall \ x$

Dấu "=" xảy ra $\Leftrightarrow \left|-\dfrac{3}{5}-x\right|=0\Leftrightarrow -\dfrac{3}{5}-x=0\Leftrightarrow x=-\dfrac{3}{5}$

Vậy $\min_A=\dfrac{2019}{2020}\Leftrightarrow x=-\dfrac{3}{5}$

$b)B=-4-|5x-2|$

Do $|5x-2| \ge 0 \ \forall \ x$

$\Rightarrow -|5x-2| \le 0 \ \forall \ x$

$\Rightarrow -|5x-2|-4 \le -4 \ \forall \ x$

Dấu "=" xảy ra $\Leftrightarrow |5x-2|=0\Leftrightarrow 5x-2=0\Leftrightarrow x=\dfrac{2}{5}$

Vậy $\max_B=-4\Leftrightarrow x=\dfrac{2}{5}.$