$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 2:\\ b.\ Gọi\ góc\ tạo\ bởi\ d\ và\ Ox\ là\ a\\ \Rightarrow tan\ a=k=1\\ \Rightarrow a=45^{o}\\ b.\ Xét\ PT\ hoành\ độ\ giao\ điểm:\\ x+1-2x+2m+1=0\\ \Leftrightarrow -x=-2m-2\\ \Leftrightarrow x=2m+2\Rightarrow y=2m+2+1=2m+3\\ \Rightarrow ( d) \cap ( d') =A( 2m+2;2m+3)\\ Để\ A\ nằm\ trong\ góc\ phần\ tư\ thứ\ II\\ \Leftrightarrow x< 0;\ y >0\\ \Leftrightarrow 2m+2< 0;\ 2m+3 >0\\ \Leftrightarrow m< \ -1;\ m >-\frac{3}{2}\\ \Leftrightarrow -\frac{3}{2} < m< -1\\ Bài\ 3:\\ a.\ \Delta '=9+m^{2} -6m=( m-3)^{2} \geqslant 0\\ \Rightarrow PT\ luôn\ có\ nghiệm\ \\ x_{1} =\frac{-6+m-3}{2} =\frac{m-9}{2} ;\\ \ x_{2} =\frac{-6-m+3}{2} =\frac{-3-m}{2}\\ hoặc\ x_{1} =\frac{-3-m}{2} ;\ x_{2} =\frac{m-9}{2}\\ \Rightarrow ( x_{1} -x_{2}) =\frac{2m-6}{2} =m-3\\ hoặc\ x_{1} -x_{2} =\frac{-2m+6}{2} =3-m\\ b.\ Theo\ Viet:\ x_{1} +x_{2} =-6;\ x_{1} x_{2} =6m-m^{2}\\ Ta\ có:\ x_{1}^{3} -x_{2}^{3} +2x_{1}^{2} +12x_{1} +72=0\\ \Leftrightarrow \ x_{1}^{3} -x_{2}^{3} +2x_{1}^{2} -2( x_{1} +x_{2}) x_{1} +72=0\\ \Leftrightarrow x_{1}^{3} -x_{2}^{3} +2x_{1}^{2} -2x_{1}^{2} -2x_{2} x_{1} +72=0\\ \Leftrightarrow x_{1}^{3} -x_{2}^{3} -2x_{2} x_{1} +72=0\\ \Leftrightarrow ( x_{1} -x_{2})\left( x_{1}^{2} +x_{2}^{2} +x_{1} x_{2}\right) -2x_{1} x_{2} +72=0\\ \Leftrightarrow ( x_{1} -x_{2})\left(( x_{1} +x_{2})^{2} -x_{1} x_{2}\right) -2x_{1} x_{2} +72=0\\ \Leftrightarrow ( x_{1} -x_{2})\left[ 36-\left( 6m-m^{2}\right)\right] -2\left( 6m-m^{2}\right) +72=0\\ \Leftrightarrow ( x_{1} -x_{2})\left( m^{2} -6m+36\right) +2m^{2} -12m+72=0\\ TH1:\ \\ ( m-3)\left( m^{2} -6m+36\right) +2m^{2} -12m+72=0\\ \Leftrightarrow m^{3} -6m^{2} +36m-3m^{2} +18m-108+2m^{2} -12m+72=0\\ \Leftrightarrow m^{3} -7m^{2} +42m-36=0\\ \Leftrightarrow m=1\\ TH2:\\ ( 3-m)\left( m^{2} -6m+36\right) +2m^{2} -12m+72=0\\ \Leftrightarrow -m^{3} +6m^{2} -36m+3m^{2} -18m+108+2m^{2} -12m+72=0\\ \Leftrightarrow -m^{3} +11m^{2} -66m+180=0\\ \Leftrightarrow m=5\\ \end{array}$
