SOLUTION: Evaluate sqrt(y/x), where x and y are positive integers, and 0 = x^5-(x^3)(y^3)-12393.

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Question 1151183: Evaluate sqrt(y/x), where x and y are positive integers, and 0 = x^5-(x^3)(y^3)-12393.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


0+=+x%5E5-%28x%5E3%29%28y%5E3%29-12393

Rewrite the equation as

x%5E3%28x%5E2-y%5E3%29+=+12393

Then find the prime factorization of 12393:

12393+=+%283%5E6%29%2817%29

So

%28x%5E3%29%28x%5E2-y%5E3%29+=+%283%5E6%29%2817%29

Since x and y are positive integers,
x%5E3=+3%5E6
means either x=3 or x=3%5E2=9.

If x=3,
%28x%5E3%29%28x%5E2-y%5E3%29+=+%2827%29%289-y%5E3%29+=+12393
which is clearly not possible.

If x=9,
%28x%5E3%29%28x%5E2-y%5E3%29+=+%28729%29%2881-y%5E3%29+=+729%2A17
81-y%5E3=17
y%5E3=64
y=4

So x=9 and y=4; and then

ANSWER: sqrt%28y%2Fx%29+=+sqrt%284%2F9%29+=+2%2F3