Question

Dau coroana !!!
Rezolvati in R sistemul de inecuatii:
a) $\left \{ {{(9x+3)(x-4)\ \textgreater \ 9 x^{2} +x+5} \atop {2x-3-(x-3) \leq 5}} \right.$
b) $\left \{ {{12 x^{2} -(2x-3)(6x+1)\ \textgreater \ x} \atop {(5x-1)(5x+1)-25 x^{2} \ \textgreater \ x-6}} \right.$

Answer 1

a)

(9x+3)(x-4)> 9x²+x+5
9x²-36x+3x-12-9x²-x-5>0

-34x-17>0
-34x>17  | *(-1)
34x<17
x< 1/2 =>S₁= x ∈ (-∞ ; 1/2) 

2x-3-(x-3)≤5
2x-3-x+3≤5
x≤5 => S₂=x∈ (-∞;5]

Sf =S₁∩ S₂= (-∞;1/2)

b)

12x²-(2x-3)(6x+1)>x
12x²-(12x²+2x-18x-3)>x

12x²-12²+16x+3-x>0

15x>-3 
x>-1/5  => S₁= x ∈ (-1/5 ; +∞)

(5x-1)(5x+1)-25x²>x-6

25x²-1-25x²-x+6>0

-x+5>0

-x>-5  | *(-5)

x<5  => S₂=x ∈ (-∞;5)

Sf =S₁∩ S₂ = (-1/5 ; 5)