# Thread: Is the following result consistent

1. ## Is the following result consistent

Is the following result consistent? Explain

$\displaystyle \sum{x^2}=64, \sum{x}=25, n=6$

2. ## Re: Is the following result consistent

Is the following result consistent? Explain
$\displaystyle \sum{x^2}=64, \sum{x}=25, n=6$
What are the indices? No one can respond without knowing what the sums are.

3. ## 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.

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

4. ## 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:
$\displaystyle \sum_{i= 0}^6 x_i^2= 64$ and $\displaystyle \sum_{i= 1}^6 x_i= 25$

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 $\displaystyle x_1= 1$, $\displaystyle x_2= 2$, $\displaystyle x_3= 3$ and $\displaystyle x_4= 4$ the equations reduce to $\displaystyle 1+ 2+ 3+ 4+ x_5+ x_6= 25$ or $\displaystyle x_5+ x_6= 15$ and $\displaystyle 1+ 4+ 9+ 16+ x_5^2+ x_6^2= 64$ or $\displaystyle x_5^2+ x_6^2= 34$. Since $\displaystyle x_5= 16- x_6$ so that $\displaystyle x^5^2+ x_6^2= x_6^2- 32x_6+ 64+ x_6^2= 34$. $\displaystyle x_6^2- 16x_6= -30$.

Was there a requirement that the numbers be integers?