Average Arithmetic Question

[Aaring23]

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.

[Sunny22uk]

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

[Sunny22uk]

Btw The formula for AM= Sum of terms/ Number of terms

[netigen]

This is not correct
(a-b)^2 = (a+b)(a-b)
This is correct
(a-b)^2= (a-b)(a-b)

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

[Sunny22uk]

Sorry for the error, post modified, thnaks for letting me know

[half2005]

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
www.pacificmath.com

[resilient]

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!