Đáp án:
\(\eqalign{
& 1)\,\,\left[ \matrix{
m > {{ - 1 + \sqrt {21} } \over 2} \hfill \cr
m < {{ - 1 - \sqrt {21} } \over 2} \hfill \cr} \right. \cr
& 2a)\,\,0 < m < {{25} \over 8} \cr
& \,\,\,b)\,\, - {1 \over 2} < k \le 1 \cr} \)
Giải thích các bước giải:
$$\eqalign{
& 1)\,\,y = \left( {{m^2} + m - 5} \right) + 2m - 1 \cr
& De\,\,ham\,\,so\,DB/R \cr
& \Rightarrow {m^2} + m - 5 > 0 \Leftrightarrow \left[ \matrix{
m > {{ - 1 + \sqrt {21} } \over 2} \hfill \cr
m < {{ - 1 - \sqrt {21} } \over 2} \hfill \cr} \right. \cr
& 2)\,\,y = - 2{x^2} + 7x - 3 \cr
& a)\,\,\left| { - 2{x^2} + 7x - 3} \right| = m\,\,co\,\,4\,\,nghiem\,\,pb \cr
& \Leftrightarrow 0 < m < {{25} \over 8} \cr
& b)\,\,\left| { - 2{x^2} + 7x - 3} \right| = 2k + 1 \cr
& \Leftrightarrow 0 < 2k + 1 \le 3 \cr
& \Leftrightarrow - 1 < 2k \le 2 \cr
& \Leftrightarrow - {1 \over 2} < k \le 1 \cr} $$
