How to do these problems?

Aug 2019
3
0
India
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?
 
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Dec 2015
972
128
Earth
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) \(\displaystyle n^3 \).
 
Aug 2019
3
0
India
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 a moderator:
Dec 2015
972
128
Earth
If they are distinct then the maximum is \(\displaystyle (n-1)n(n+1)\).
 
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Aug 2019
3
0
India
Do you know how to do the first problem?
 
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