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) -Dan
Last edited by topsquark; Aug 17th 2014 at 02:59 PM. Reason: Need a course on basic spelling!
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Hint: Spoiler: Let . What is 1/y? -Dan
No takers this time? Here's my solution: Spoiler: Let Then Putting this into the original equation gives: Multiplying both sides by gives: or 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 . -Dan
Last edited by topsquark; Aug 24th 2014 at 03:45 PM.
But the answer should be which leads to
Last edited by Idea; Aug 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! -Dan
Last edited by topsquark; Aug 24th 2014 at 03:46 PM.
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