Cho hai tập A = [0; 5] B = (2a; 3a + 1), a > –1. Với giá trị nào của a thì \[{\rm{A}} \cap {\rm{B}} \ne \emptyset \].
Cho hai tập A = [0; 5] B = (2a; 3a + 1), a > –1. Với giá trị nào của a thì \[{\rm{A}} \cap {\rm{B}} \ne \emptyset \].
A. \[\left[ \begin{array}{l}{\rm{a}} < \frac{5}{2}\\{\rm{a}} \ge - \frac{1}{3}\end{array} \right.\];
B. \(\left[ \begin{array}{l}{\rm{a}} \ge \frac{5}{2}\\{\rm{a}} < - \frac{1}{3}\end{array} \right.\);
C. \( - \frac{1}{3} \le {\rm{a}} < \frac{5}{2}\);
D. \[ - \frac{1}{3} \le {\rm{a}} \le \frac{5}{2}\].
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Điều này xảy ra khi $2a < 5$ và $3a+1 > 0$.
Ta có:
$2a < 5 \Leftrightarrow a < \frac{5}{2}$
$3a + 1 > 0 \Leftrightarrow 3a > -1 \Leftrightarrow a > -\frac{1}{3}$
Kết hợp với điều kiện $a > -1$, ta có $- \frac{1}{3} < a < \frac{5}{2}$.
Vì $B = (2a; 3a+1)$ là khoảng, nên dấu "=" không xảy ra.
Vậy đáp án là $ - \frac{1}{3} \le {\rm{a}} < \frac{5}{2}$
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