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August 13th, 2019, 05:50 AM   #1
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Question 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.
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August 13th, 2019, 06:33 AM   #2
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Quote:
Originally Posted by Puku View Post
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 $.
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August 13th, 2019, 06:44 AM   #3
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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.
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August 13th, 2019, 06:50 AM   #4
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If they are distinct then the maximum is $\displaystyle (n-1)n(n+1)$.
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August 13th, 2019, 07:08 AM   #5
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Do you know how to do the first problem?

Last edited by skipjack; August 13th, 2019 at 08:09 AM.
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August 13th, 2019, 08:02 AM   #6
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