Question

Неравенство......................................

Answer 1

$frac{ x^{2} }{3} geq frac{3x+3}{4}$

$frac{ x^{2} }{3} - frac{3x+3}{4} geq 0$

$frac{4 x^{2} -3(3x+3)}{12} geq 0$

$frac{4 x^{2} -9x-9}{12} geq 0$   *12

${4 x^{2} -9x-9} geq 0$

${4 x^{2} -9x-9} =0$

$D=(-9)^2-4*4*9=81+144=225$

$x_1= frac{9+15}{8}=3$

$x_2= frac{9-15}{8}=-0.75$

$4(x-3)(x+0.75) geq 0$

Решаем методом интервалов:

-----------+---------[-0.75]------- - --------[3]---------+------------

Ответ: $(-$∞$;-0.75]$ ∨ $[3;+$∞$)$