Question

If x, m satisfy the inequality log_1/2 x²≥ log_1/2

(x + 2) and 49 x² – 4m⁴≤ 0 then

• A. m ∈ (– ∞, 1) ∪ (1, ∞)
• B. m∈ (– ∞, –$\sqrt{5}$) ∪ ($\sqrt{5}$, ∞)
• C. m∈ (– ∞, –$\sqrt{7}$) ∪ [$\sqrt{7}$, ∞)
• D. None

Answer 1

Answer: (D)

None

Answer 2

log_1/2 x² ≥ log_1/2 (x + 2)

⇒ x² – x – 2 ≤ 0

x ∈ [–1, 2] ~ {0}

& 49x² ≤ 4m⁴

⇒ $–\frac{2}{7}$ m² ≤ x ≤ $\frac{2}{7}$ m²

m∈ $\left\lbrack \frac{–\sqrt{7}}{2},\frac{\sqrt{7}}{2} \right\rbrack$ ~ {0}