Question

for what vaue of b the inequality bsquare+8b>=9b+14 is correctfor what vaue of b the inequality bsquare+8b>=9b+14 is correct

Answer 1

This question is based on inequality. just treat the question like simple algebra and then use inequality concepts.

b² + 8b ≥ 9b + 14

or, b² + 8b - 9b - 14 ≥ 0

or, b² - b - 14 ≥ 0

use quadratic formula, b = { 1 ± √(1 + 56)}/2

b = {1 ± √57}/2

or, {b - (1 + √57)/2}{b - (1 - √57)/2} ≥ 0

solve this inequality ,

hence, b $\in$ [(1 + √57)/2, ∞) U (-∞ , (1 - √57)/2]