Question

The solution set of the inequation log_1/3(x² + x + 1) + 1 > 0 is ______.

Options

• (–∞, –2) U (1, + ∞)

• [–1, 2]

• (–2, 1)

• (–∞, + ∞)

Answer 1

The solution set of the inequation log_1/3(x² + x + 1) + 1 > 0 is (–2, 1).

Explanation:

log_1/3(x² + x + 1) > –1

⇒ `x^2 + x + 1 < (1/3)^-1`

x² + x + 1 > 0

⇒ x ∈ R

⇒ x² + x + 1 < 3

⇒ x² + x – 2 < 0

⇒ (x – 1)(x + 2) < 0

⇒ x ∈ (–2, 1)