Question

решите неравенство -2x²-5x+3<0

Answer 1

$\displaystyle -2x^2-5x+3<0\\-2x^2+x-6x+3<0\\-x(2x-1)-3(2x-1)<0\\-(2x-1)(x+3)<0\\(2x-1)(x+3)>0\\\\ \left \{ {{2x-1>0} \atop {x+3>0}} \right.=\left \{ {{x>\frac{1}{2} } \atop {x>-3}} \right.=x\in (\frac{1}{2}, + \infty)\\\\ \left \{ {{2x-1<0} \atop {x+3<0}} \right.=\left \{ {{x<\frac{1}{2} } \atop {x<-3}} \right.=x \in (- \infty,-3)\\\\ x \in (- \infty,-3) \cup (\frac{1}{2}, +\infty)$