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 August 13th, 2019, 05:50 AM #1 Newbie   Joined: Aug 2019 From: India Posts: 3 Thanks: 0 How to do these problems? 1) Given that x = 2a^5 = 3a^2, what is the smallest possible value of x? 2) Suppose 3 distinct numbers are chosen from 1,2,.....,3n with their sum equal to 3n. What is the largest possible product of these numbers? Last edited by skipjack; August 13th, 2019 at 07:53 AM.
August 13th, 2019, 06:33 AM   #2
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Quote:
 Originally Posted by Puku 1)Given that x = 2a^5 = 3a^2 , what is the smallest possible value of x? 2)Suppose 3 distinct numbers are chosen from 1,2,.....,3n with their sum equal to 3n.What is the largest possible product of these numbers?
2) $\displaystyle n^3$.

 August 13th, 2019, 06:44 AM #3 Newbie   Joined: Aug 2019 From: India Posts: 3 Thanks: 0 Uh, okay but I mentioned in the second problem that the numbers are distinct; are you sure it's n^3? It would be better if you show me the steps how you got n^3. Last edited by skipjack; August 13th, 2019 at 07:58 AM.
 August 13th, 2019, 06:50 AM #4 Senior Member   Joined: Dec 2015 From: somewhere Posts: 708 Thanks: 96 If they are distinct then the maximum is $\displaystyle (n-1)n(n+1)$. Thanks from Puku
 August 13th, 2019, 07:08 AM #5 Newbie   Joined: Aug 2019 From: India Posts: 3 Thanks: 0 Do you know how to do the first problem? Last edited by skipjack; August 13th, 2019 at 08:09 AM.
 August 13th, 2019, 08:02 AM #6 Global Moderator   Joined: Dec 2006 Posts: 21,015 Thanks: 2250 1) 0

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