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Average Arithmetic Question

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by Aaring23 » Thu Apr 24, 2008 12:20 pm
Hey guy's I was wondering if someone could help me out with this problem. Here is the problem.

Which of the following is equal to the average (arithmetic mean) of (x + 2)^2 and (x - 2)^2.

Answer is X^2 + 4.



Any help would be greatly appreciated. Thank you.
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by Sunny22uk » Thu Apr 24, 2008 12:54 pm
the formula used here was (a+b)^2= A^2 + B^2 +2ab
and (a-b)^2= A^2 + B^2 -2ab
You can expand the equation, you will get the answer
in this case a will be x and b will be 2
Hope this helps
Cheers
Last edited by Sunny22uk on Thu Apr 24, 2008 6:05 pm, edited 2 times in total.
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by Sunny22uk » Thu Apr 24, 2008 12:54 pm
Btw The formula for AM= Sum of terms/ Number of terms
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by netigen » Thu Apr 24, 2008 2:43 pm
This is not correct
(a-b)^2 = (a+b)(a-b)
This is correct
(a-b)^2= (a-b)(a-b)
Sunny22uk wrote:1)the formula used here was (a+b)^2= A^2 + B^2 +2ab
and (a-b)^2= A^2 + B^2 -2ab
You can expand the equation, you will get the answer
2) the second option is to write (a+b)^2 as (a+B)(a+b) and write (a-b)^2= (a+b)(a-b),take (a+b) common and solve the equation.
in this case a will be x and b will be 2
Hope this helps
Cheers
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by Sunny22uk » Fri Apr 25, 2008 5:38 am
Sorry for the error, post modified, thnaks for letting me know :)
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better suggestion

by half2005 » Fri Apr 25, 2008 7:03 am
Hi,

I suggest that every time you post a question, you try posting all of the answers given to you. This way we will have a better solutions (shortcuts) for you.
In thisp roblem you will be getting x^2 + 4x +4 + x^2 -2x + 4 = 2x^2 + 8 and then divide this answer by 2 to get (2x^2 +8)/2 = 2x^2/2 + 8/2 = x^2 + 4.

MO
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average

by resilient » Sun Apr 27, 2008 1:01 am
when expanding these two, are we dividing by 4 or 2. THe reason why I ask this is when expanded it can become 4. Curious!
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