Question

sa se afle a astfel incat inecuatia 2x^2+2x+3/x^2+x+1<a oricare ar fi a inclus in R​

Answer 1

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 , +∞)