Giải các bất phương trình, hệ bất phương trình (ẩn m) sau:
a) \(\left\{ \matrix{
{(2m – 1)^2} – 4({m^2} – m) \ge 0 \hfill \cr
{1 \over {{m^2} – m}} > 0 \hfill \cr
{{2m – 1} \over {{m^2} – m}} > 0 \hfill \cr} \right.;\)
{(m – 2)^2} – (m + 3)(m – 1) \ge 0 \hfill \cr
{{m – 2} \over {m + 3}} > 0 \hfill \cr
{{m – 1} \over {m + 3}} > 0 \hfill \cr} \right.\)
Gợi ý làm bài
a) \(\eqalign{
& \left\{ \matrix{
{(2m – 1)^2} – 4({m^2} – m) \ge 0 \hfill \cr
{1 \over {{m^2} – m}} > 0 \hfill \cr
{{2m – 1} \over {{m^2} – m}} > 0 \hfill \cr} \right. \cr
& \Leftrightarrow \left\{ \matrix{
1 \ge 0 \hfill \cr
{m^2} – m > 0 \Leftrightarrow m > 1 \hfill \cr
2m – 1 > 0 \hfill \cr} \right. \cr} \)
b) \(\eqalign{
& \left\{ \matrix{
{(m – 2)^2} – (m + 3)(m – 1) \ge 0 \hfill \cr
{{m – 2} \over {m + 3}} > 0 \hfill \cr
{{m – 1} \over {m + 3}} > 0 \hfill \cr} \right. \cr
& \Leftrightarrow \left\{ \matrix{
– 6m + 7 \ge 0 \hfill \cr
(m – 2)(m + 3) < 0 \hfill \cr
(m – 1)(m + 3) > 0 \hfill \cr} \right. \cr} \)
\( \Leftrightarrow \left\{ \matrix{
m \le {7 \over 6} \hfill \cr
– 3 < m < 2 \hfill \cr
\left[ \matrix{
m > 1 \hfill \cr
m < – 3 \hfill \cr} \right. \hfill \cr} \right. \Leftrightarrow 1 < m \le {7 \over 6}\)