# Is the following result consistent

• May 2nd 2013, 10:23 AM
Is the following result consistent
Is the following result consistent? Explain

$\sum{x^2}=64, \sum{x}=25, n=6$
• May 2nd 2013, 10:54 AM
Plato
Re: Is the following result consistent
Quote:

Is the following result consistent? Explain
$\sum{x^2}=64, \sum{x}=25, n=6$

What are the indices? No one can respond without knowing what the sums are.
• May 2nd 2013, 11:24 AM
Re: Is the following result consistent
It was set in a university exam. I am also confused. We have to search six numbers whose sum is 25 and sum of squares of those six numbers is 64.

Quote:

Originally Posted by Plato
What are the indices? No one can respond without knowing what the sums are.

• May 2nd 2013, 11:50 AM
HallsofIvy
Re: Is the following result consistent
Since it includes the information that "n= 6", I would interpret this as summing over 6 terms- and assume that the sums run from 1 to 6:
$\sum_{i= 0}^6 x_i^2= 64$ and $\sum_{i= 1}^6 x_i= 25$

So the question is "do there exist 6 numbers, that sum to 25, whose squares sum to 64?"

That is 6 numbers determined by only two equations so it seems to me there ought to be many ways to do that. For example, if we choose to take $x_1= 1$, $x_2= 2$, $x_3= 3$ and $x_4= 4$ the equations reduce to $1+ 2+ 3+ 4+ x_5+ x_6= 25$ or $x_5+ x_6= 15$ and $1+ 4+ 9+ 16+ x_5^2+ x_6^2= 64$ or $x_5^2+ x_6^2= 34$. Since $x_5= 16- x_6$ so that $x^5^2+ x_6^2= x_6^2- 32x_6+ 64+ x_6^2= 34$. $x_6^2- 16x_6= -30$.

Was there a requirement that the numbers be integers?