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Just count them ! (Posted on 2019-04-09) Difficulty: 2 of 5
How many integer solutions has the following equation:
sqrt(x)+sqrt(y)=sqrt(3888)?

Assume x>y.

See The Solution Submitted by Ady TZIDON    
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Solution Analytic Solution Comment 2 of 2 |
3888 = 36^2 * 3.  Then x and y can be reduced to the form a*sqrt(3) and b*sqrt(3). The compound constraint a>b>=0 follows from x>y and the fact we are taking square roots.

Then a+b = 36.  There are 19 ways to express 36 as an ordered sum of two nonnegative integers.  One of these is 18+18, which fails the a>b requirement so the answer to the problem is 18 integer solutions.

  Posted by Brian Smith on 2019-04-09 12:05:54
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