+0

# Inequality

0
103
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?

May 23, 2022

#1
+118135
+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

May 23, 2022
edited by Melody  May 23, 2022