Question

rezolvati va rog sistemul de inecuatii
{12x² - (2x-3) (6x+1) >x
{ (5x -1 ) ( 5x+1) - 25x² >x - 6

Answer 1

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Answer 2

$\left \{ {{12 x^{2} -(2x-3)(6x+1)>x} \atop {(5x-1)(5x+1)- 25x^{2} >x-6}} \right.$

Rezolvam prima inegalitate a sistemului:

$12x^{2} -(2x-3)(6x+1)>x<=> \\ <=> 12x^{2}-(12 x^{2} +2x-18x-3)>x<=> \\ <=>12 x^{2} -(12 x^{2} -16x-3)>x<=> \\ <=> 12 x^{2} -12 x^{2} +16x+3>x<=> \\ <=>16x+3>x<=> \\ <=>15x>-3=>x> -\frac{1}{5} .$

Rezolvam a doua inegalitate a sistemului:

$(5x-1)(5x+1)- 25x^{2} >x-6<=> \\ <=>25 x^{2} -1-25 x^{2} >x-6<=> \\ <=>-1>x-6 <=>\\ <=>5>x$

Avem: $x> -\frac{1}{5} ~si~x<5$ => x∈ $( -\frac{1}{5};5)$.