Let a be the smallest integer satisfying the inequality x^2 - 15 < 2x, and let b be the largest integer satisfying the same inequality. What is b-a?

Guest May 23, 2022

#1**+1 **

Let a be the smallest integer satisfying the inequality x^2 - 15 < 2x, and let b be the largest integer satisfying the same inequality. What is b-a?

\(x^2 - 15 < 2x\\ x^2 - 15 -2x <0\\ x^2 -2x - 15 <0\\\)

This is a concave up parabola

It will be less than 0 between the roots

the roots are

\(x = {2 \pm \sqrt{4+60} \over 2}\\ x = {2 \pm 8 \over 2}\\ x=1\pm4 \)

the equation is satified for all x values between -3 and 5 BUT NOT inclusive of -3 and 5)

So the smallest integer is a=-2 and the largest is b=4

4 - - 2 = 6

Melody May 23, 2022