Here's a more straightforward problem for College Algebra level.
Let a > 1 be an integer. Find all integers x, such that
(Source: Singapore Mathematics Olympiad)
Last edited by topsquark; August 17th 2014 at 02:59 PM.
Reason: Need a course on basic spelling!
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Let . What is 1/y?
No takers this time? Here's my solution: Spoiler:
Putting this into the original equation gives:
Multiplying both sides by gives:
This is a quadratic equation in so we may apply the quadratic formula:
After some simplification we get
So we have two cases: , which leads to x = 2,
or , which leads to x = -2.
You can easily back-substitute and you will find that both solutions fit the original equation, so .
Last edited by topsquark; August 24th 2014 at 03:45 PM.
But the answer should be
which leads to
Last edited by Idea; August 24th 2014 at 08:10 AM.
Originally Posted by Idea But the answer should be
which leads to I have fixed the problem in my derivation. Thanks for the catch!
Last edited by topsquark; August 24th 2014 at 03:46 PM.
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