Răspuns:
(2x²+2x+3)/(x²+x+1) < a
(2x²+2x+2 +1)/(x²+x+1) < a
(2x²+2x+2)/(x²+x+1) + 1/(x²+x+1) < a
2(x²+x+1)/(x²+x+1) + 1/(x²+x+1) < a se simplifica (x²+x+1) in prima ecuatie
2 + 1/(x²+x+1) < a
Discutie
x²+x > 0 pentru ca x² >x
1 >0 => x²+x+1 ≥0 oricare ar fi x∈R
dar x²+x+1 ≥1
=> 1/(x²+x+1) ≤ 1
=>2 + 1/x²+x+1 ≤ 3
si 2 + 1/(x²+x+1) < a
=> a>3 , a∈(3 , +∞)
