Giải các bất phương trình sau:
a) \(\left\{ \matrix{
{x^2} \ge 0,25 \hfill \cr
{x^2} – x \le 0 \hfill \cr} \right.;\)
b) \(\left\{ \matrix{
(x – 1)(2x + 3) > 0 \hfill \cr
(x – 4)(x + {1 \over 4}) \le 0 \hfill \cr} \right.\)
Gợi ý làm bài
a) \(\left\{ \matrix{
{x^2} \ge 0,25 \hfill \cr
{x^2} – x \le 0 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
{x^2} – 0,25 \ge 0 \hfill \cr
{x^2} – x \le 0 \hfill \cr} \right. \Leftrightarrow 0,5 \le x \le 1.\)
b) \(\eqalign{
& \left\{ \matrix{
(x – 1)(2x + 3) > 0 \hfill \cr
(x – 4)(x + {1 \over 4}) \le 0 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
x \in ( – \infty ; – {3 \over 2}) \cup (1; + \infty ) \hfill \cr
x \in {\rm{[ – }}{1 \over 4}{\rm{;4]}} \hfill \cr} \right. \cr
& \Leftrightarrow x \in (1;4]. \cr} \)