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# help inequality

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Let a be the smallest integer satisfying the inequality x^2 - 15 < 12x, and let b be the largest integer satisfying the same inequality. What is b-a?

Jan 16, 2022

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What is b-a?

Hello Guest!

x^2 - 15 < 12x

$$x^2-12x-15=0\\ x=6\pm\sqrt{36+15}\\ x_{max}=13.141...\\ x_{min}=-1.141...$$

a > $$x_{min}$$

a = - 1

b < $$x_{max}$$

b = 13

$${\color{blue}b-a}=13-(-1)\color{blue}=14$$

!

Jan 16, 2022
edited by asinus  Jan 16, 2022
edited by asinus  Jan 16, 2022