Question

lf x is real, the maximum value of `(3x^2 + 9x + 17)/(3x^2 + 9x + 7)` is ______.

Options

• `1/4`

• 41

• 1

• `17/7`

Answer 1

lf x is real, the maximum value of `(3x^2 + 9x + 17)/(3x^2 + 9x + 7)` is 41.

Explanation:

Let y = `(3x^2 + 9x + 17)/(3x^2 + 9x + 7)`

3x²(y – 1) + 9x(y – 1) + 7y – 17 = 0

D ≥ 0  ...[∵ x is real]

81(y – 1)² – 4 × 3(y – 1)(7y – 17) ≥ 0

⇒ (y – 1)(y – 41) ≤ 0

⇒ 1 ≤ y ≤ 41

∴ Max value of y is 41