[tex] \left \{ {{12 x^{2} -(2x-3)(6x+1)>x} \atop {(5x-1)(5x+1)- 25x^{2} >x-6}} \right. [/tex]
Rezolvam prima inegalitate a sistemului:
[tex] 12x^{2} -(2x-3)(6x+1)>x<=> \\ <=> 12x^{2}-(12 x^{2} +2x-18x-3)>x<=> \\ <=>12 x^{2} -(12 x^{2} -16x-3)>x<=> \\ <=> 12 x^{2} -12 x^{2} +16x+3>x<=> \\ <=>16x+3>x<=> \\ <=>15x>-3=>x> -\frac{1}{5} .[/tex]
Rezolvam a doua inegalitate a sistemului:
[tex](5x-1)(5x+1)- 25x^{2} >x-6<=> \\ <=>25 x^{2} -1-25 x^{2} >x-6<=> \\ <=>-1>x-6 <=>\\ <=>5>x[/tex]
Avem: [tex]x> -\frac{1}{5} ~si~x<5[/tex] => x∈ [tex]( -\frac{1}{5};5) [/tex].
