Question

Help!
Sa se det solutiile reale ale ecuatiei
2x+3
________mai mare sau egal cu 1
X^2 + x+1

Answer 1

(2x+3)/(x^2+x+1)≥1 ⇔

[2x+3-(x^2+x+1)]/(x^2+x+1)≥0 ⇔

(-x^2+x+2)/(x^2+x+1)≥0 ⇔

(x^2-x-2)/(x^2+x+1)≤0

x^2+x+1≥0 ⇒ x^2-x-2≤0 ⇔

(x-2)(x+1)≤0⇒x∈[-1;2]