Toán Lớp 7: có bao nhiêu số nguyên thỏa mãn x
|x-4|+|5-x|=1
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Toán Lớp 7: có bao nhiêu số nguyên thỏa mãn x
|x-4|+|5-x|=1
Comments ( 1 )
Do:\left| a \right| + \left| b \right| \ge \left| {a + b} \right|\\
\Leftrightarrow \left| {x – 4} \right| + \left| {5 – x} \right| \ge \left| {x – 4 + 5 – x} \right|\\
\Leftrightarrow \left| {x – 4} \right| + \left| {5 – x} \right| \ge \left| 1 \right| = 1
\end{array}$
\left\{ \begin{array}{l}
x – 4 \ge 0\\
5 – x \ge 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \ge 4\\
x \le 5
\end{array} \right. \Leftrightarrow 4 \le x \le 5\\
Do:x \in Z\\
\Leftrightarrow x = 4;x = 5
\end{array}$