Question 1209288
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Find the number of integers n that satisfy n^2 < 144 + 24n.
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<pre>
This given inequality

   n^2 < 144 + 24n


is equivalent to

    n^2 - 24n < 144

    n^2 - 24n + 144 < 144 + 144

    (n-12)^2 < 288

    |n-12| < sqrt(288) = 16.97...

    -16.97... < n-12 < 16.97...


Since we look for integer solutions, the last inequality implies


     -16 <= n-12 <= 16.


It has 16 + 1 + 16 = 33 different solutions for integer n-12.


Hence, the original inequality, given in the problem, has 33 different integer solutions.    <U>ANSWER</U>
</pre>

Solved.