$\displaystyle \begin{array}{{>{\displaystyle}l}} 1.\\ a.\ \frac{-x^{2} +5x+6}{x-3} >0\\ Quan\ sat\ BXD\Leftrightarrow S=( -1;3) \cup ( 6;+\infty )\\ b.\ \frac{\pi }{2} < a< \pi \Rightarrow sina< 0,\ cosa >0\\ 1+tan^{2} a=\frac{1}{cos^{2} a} \Rightarrow cos^{2} a=\frac{1}{6}\\ \Rightarrow cosa=\frac{1}{\sqrt{6}} \ ( Do\ cosa >0)\\ \Rightarrow sina=tana.cosa=\frac{-\sqrt{5}}{\sqrt{6}}\\ \Rightarrow sin2a=2sinacosa=\frac{-\sqrt{5}}{3}\\ 2.\\ a.\ AH\ di\ qua\ A( -2;-1) \ nhan\ \overrightarrow{BC}( 4;-3) \ la\ VTPT\\ AH:\ 4( x+2) -3( y+1) =0\\ hay\ AH:4x-3y+5=0\\ b.\ BC\ di\ qua\ C( 5;0) \ nhan\ \overrightarrow{BC}( 4;-3) \ là\ vtcp\\ BC:\frac{x-5}{4} =-\frac{y}{3} \ hay\ BC:\ 3x+4y-15\\ \ Ban\ kinh\ R=d( A;BC) =\frac{|3.-2+4.-1-15|}{\sqrt{3^{2} +4^{2}}} =5\\ ( C) \ có\ tam\ A( -2;-1) ,\ ban\ kinh\ R=5\\ ( C) :\ ( x+2)^{2} +( y+1)^{2} =25\\ 3.\ BPT\ co\ nghiem\ \forall x\in \mathbb{R} \Leftrightarrow \{_{\vartriangle < 0}^{a >0}\\ \Leftrightarrow \vartriangle =4( m-1)^{2} -4.3.( m+5) < 0\\ \Leftrightarrow m^{2} -2m+1-3m-15< 0\\ \Leftrightarrow m^{2} -5m-14< 0\\ \Leftrightarrow -2< m< 7\\ Vay\ S=( -2;7) \end{array}$
