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musicgold
Posts:
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Registered:
4/16/09


Finding rational square roots
Posted:
Apr 23, 2012 6:13 PM


Hi,
I am struggling with this puzzle from a book.
Puzzle : Can you find a number n such that, the numbers n7, n, and n+7 have rational square roots (can be expressed as integers or fractions)? According to the book one of the solution is n =113569 /14400
This is what I have done so far:
Let p, q, r be the square roots of n7, n, and n+7, respectively.
(n7) * n * (n+7) = p^2 * q^2 * r^2
n^3 49n = p^2 * q^2 * r^2
As I have 4 unknowns and only one equation, I do not know how to proceed from here. What should I do?
Thanks.
Message was edited by: musicgold



