Đáp án:
$1) \left\{\begin{array}{l} x=3,5\\y=4,5\end{array} \right.\\ 2) \left\{\begin{array}{l} x=-\dfrac{2}{3}\\y=\dfrac{3}{4}\\z=5\end{array} \right.\\ 3)\text{Vô nghiệm}\\ 4)\left\{\begin{array}{l} x=\dfrac{2}{3}\\y=-\dfrac{17}{12}\\z=-\dfrac{9}{4}\end{array} \right.$
Giải thích các bước giải:
$1)$
Do $|x-3,5| \ge 0 \ \forall \ x;|4,5-y|\ge 0 \ \forall \ y$
$\Rightarrow |x-3,5|+|4,5-y|\ge 0 \ \forall \ x,y$
Dấu "=" xảy ra $\Leftrightarrow \left\{\begin{array}{l} x-3,5=0\\4,5-y=0\end{array} \right. \Leftrightarrow \left\{\begin{array}{l} x=3,5\\y=4,5\end{array} \right.$
$2)$
Do $\left|x+\dfrac{2}{3}\right| \ge 0 \ \forall \ x;\left|y-\dfrac{3}{4}\right|\ge 0 \ \forall \ y;|z-5| \ge 0 \ \forall \ z$
$\Rightarrow \left|x+\dfrac{2}{3}\right| +\left|y-\dfrac{3}{4}\right|+|z-5| \ge 0 \ \forall \ x,y,z$
Dấu "=" xảy ra $\Leftrightarrow \left\{\begin{array}{l} x+\dfrac{2}{3}=0\\y-\dfrac{3}{4}=0\\z-5=0\end{array} \right. \Leftrightarrow \left\{\begin{array}{l} x=-\dfrac{2}{3}\\y=\dfrac{3}{4}\\z=5\end{array} \right.$
$3)$
$|x-2|+|3-x| \ge |x-2+3-x|=1$
$\Rightarrow |x-2|+|3-x| =0$ vô nghiệm
$4)$
Do $\left|x-\dfrac{2}{3}\right| \ge 0 \ \forall \ x;\left|x+y+\dfrac{3}{4}\right|\ge 0 \ \forall \ x,y;\left|y-z-\dfrac{5}{6}\right| \ge 0 \ \forall \ y,z$
$\Rightarrow \left|x-\dfrac{2}{3}\right| +\left|x+y+\dfrac{3}{4}\right|+\left|y-z-\dfrac{5}{6}\right| \ge 0 \ \forall \ y,z| \ge 0 \ \forall \ x,y,z$
Dấu "=" xảy ra $\Leftrightarrow \left\{\begin{array}{l} x-\dfrac{2}{3}=0\\x+y+\dfrac{3}{4}=0\\y-z-\dfrac{5}{6}=0\end{array} \right. \Leftrightarrow \left\{\begin{array}{l} x=\dfrac{2}{3}\\y=-x-\dfrac{3}{4}\\z=y-\dfrac{5}{6}\end{array} \right.\Leftrightarrow \left\{\begin{array}{l} x=\dfrac{2}{3}\\y=-\dfrac{17}{12}\\z=-\dfrac{9}{4}\end{array} \right.$
