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?
What is b-a?
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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
\({\color{blue}b-a}=13-(-1)\color{blue}=14\)
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