Which of the following is equal to the average (arithmetic mean) of (x

Question

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

A. x^2
B. x^2 + 2
C. x^2 + 4
D. x^2 + 2x
E. x^2 + 4x

gmatdog · Answer

Answer C.

Avg =   / 2

Expanding and simplifying, (x^2 + 4x + 4 + x^2 - 4x + 4 ) / 2 = x^2 + 4

cyberjadugar · Answer

Hi,

\frac{(x+2)^2 + (x-2)^2}2 
 =\frac{(x^2+2x+4) + (x^2-2x+4)}2 
 =x^2+4

Answer (C)

Regards,

damstamnd · Answer

Answer: C

The arithmetic mean is the sum of the elements divided by the number of elements.

stonecold · Answer

The sum of (x+2)^2 and (x-2)^2 = 2x^2+8
Hence Average = x^2+4

Hence C

Abhishek009 · Answer

AM of (x+2)^2 +(x-2)^2

=  \frac{( x^2 + 4x + 4 ) + ( x^2 - 4x + 4 )}{2}

=  \frac{2x^2 + 8}{2}

=  x^2 + 4

Hence, answer will be (C)  x^2 + 4

Grid · Answer

please I found answer B. because I factorized the expression (x+2)^2 = (x+2)(x-2) instead of (x+2)^2=(x-2)(x-2)
I used the algeabric formula of (a-b)^2=(a-b)(a+b) so my question is, how do I recognize when an expression of (a-b)^2 is equals to (a-b)(a+b) ?
Thank you in advance

theLucifer · Answer

The equations should be valid for all value of X .. so let x=0 in the equations.. 
We get (0+2)^2=4 and (0-2)^2=4
Average of these two numbers =4

Only Ans (C) gives us this value

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kanusha · Answer

x^{2} + 4 + 2X + X^{2} + 4 -2X

\frac{2X^{2} + 8}{2}

\frac{2}{2} (X^{2} + 4)

C

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Which of the following is equal to the average (arithmetic mean) of (x

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Which of the following is equal to the average (arithmetic mean) of (x

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