Question

The least integer a, for which

1 + log₅ (x² + 1) £ log₅ (ax² + 4x + a) is true for all x Î R is –

• A. 6
• B. 7
• C. 10
• D. 1

Answer 1

Answer: (B)

7

Answer 2

Inequality ax² + 4x + a > 0 is possible if a > 0

and 16 – 4a²

< 0 ̃ a > 2

log₅ 5 + log₅ (x² + 1) £ log₅ (ax² + 4x + a)

5(x² + 1) £ ax² + 4x + a

(a – 5) x² + 4x + (a – 5) > 0 it hold if a – 5 > 0 and 16 – 4

(a – 5)⁵ ³ 0

a > 5 and a £ 3 or, a ³ 7 ̃ a ³ 7 ̃ a Î [7, ¥)