Question

Решите неравенство x^2/2<2x+2/3

Answer 1

$frac{ x^{2} }{2} <2x + frac{2}{3}$
$x^{2} <4x+ frac{4}{3}$
$x^{2} -4x- frac{4}{3} <0$
$3x^{2} -12x- 4 <0$
D=144+48=192
$x1= frac{12+ sqrt{192} }{6} = frac{4(3+ sqrt{12} )}{6} = frac{2(3+ sqrt{12} )}{3}$
$x2= frac{2(3- sqrt{12} )}{3}$

+++++x2--------x1+++++++
Ответ:$( frac{2(3- sqrt{12}) }{3};frac{2(3+ sqrt{12}) }{3} )$