Question

Solution set of inequality

log₁₀(x² – 2x – 2) £ 0 is –

• A. [– 1, 1 – $\sqrt{3}$]
• B. [1 + $\sqrt{3}$, $\sqrt{3}$]
• C. [– 1, 1 – $\sqrt{3}$] È [1 + $\sqrt{3}$, 3]
• D. None of these

Answer 1

Answer: (C)

– 1, 1 – $\sqrt{3}$$$ È 1 + $\sqrt{3}$, 3$$

Answer 2

Given log₁₀(x² – 2x – 2) £ 0

̃ x² – 2x – 2 £ 10⁰

̃ x² – 2x – 3£ 0

̃ – 1 £ x £ 3 …….(1)

For logarithm to be defined.

x² – 2x – 2 > 0

̃ x < 1 – $\sqrt{3}$

or x > 1 + $\sqrt{3}$ …….(2)

From (1) and (2), common values of x are given by

–1 £ x £ 1 – $\sqrt{3}$

or 1 + $\sqrt{3}$ < x £ 3