Question

3x^2 ≥ | x^2+2x | + 12

Answer 1

$3x^2geq |x^2+2x|+12$

$left { {{x^2+2xgeq0} atop {3x^2geq x^2+2x+12}} right.$ 

$left { {{x(x+2)geq0} atop {x^2-x-6geq 0}} right.$

$left { {{x(-infty;-2]cup[0;+infty)} atop {x^2-x-6geq 0}} right.$

D = 25

x = 3

x = -2

  

$left { {{x^2+2x<0} atop {3x^2geq -x^2-2x+12}} right.$ 

$left { {{x(x+2)<0} atop {2x^2+x-6geq 0}} right.$

$left { {{x(-2;0)} atop {2x^2-x-6geq 0}} right.$

D = 49

x = 3/2 - не принадлежит области определения

x = -2

 

Ответ: x = -2; x = 3