Question

решите неравенство 3-2х-х^2>0​

Answer 1

$\displaystyle 3-2x-x^2 > 0\\-x^2-2x+3 > 0\\-x^2+x-3x+3 > 0\\-x(x-1)-3(x-1) > 0\\-(x-1)(x+3) > 0\\(x-1)(x+3) < 0\\\\\left \{ {{x-1 < 0} \atop {x+3 > 0}} \right. \rightarrow \left \{ {{x < 1} \atop {x > -3}} \right. \rightarrow x \in (-3,1)\\\\\left \{ {{x-1 > 0} \atop {x+3 < 0}} \right. \rightarrow \left \{ {{x > 1} \atop {x < -3}} \right. \rightarrow \oslash\\\\x \in(-3,1)$