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# Which of the following is equal to the average (arithmetic

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Which of the following is equal to the average (arithmetic [#permalink]

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16 Jun 2012, 20:42
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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
[Reveal] Spoiler: OA

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Re: which of the following is equal avg (x+2)^2 and (x-2)^2 [#permalink]

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16 Jun 2012, 21:42

Avg = [(x+2)^2 + (x-2)^2] / 2

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

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Re: which of the following is equal avg (x+2)^2 and (x-2)^2 [#permalink]

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16 Jun 2012, 21:55
jsphcal wrote:
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

this was taken from a powerprep question

Hi,

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

Regards,

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Re: Which of the following is equal to the average (arithmetic [#permalink]

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17 Jun 2012, 10:21

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

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Re: Which of the following is equal to the average (arithmetic [#permalink]

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18 Dec 2016, 15:40
The sum of (x+2)^2 and (x-2)^2 = 2x^2+8
Hence Average = x^2+4

Hence C

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Re: Which of the following is equal to the average (arithmetic [#permalink]

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19 Dec 2016, 10:58
jsphcal wrote:
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

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) $$x^2 + 4$$
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Re: Which of the following is equal to the average (arithmetic [#permalink]

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25 Dec 2016, 19:29
Abhishek009 wrote:
jsphcal wrote:
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

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) $$x^2 + 4$$

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) ?

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Re: Which of the following is equal to the average (arithmetic [#permalink]

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25 Dec 2016, 20:12
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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Re: Which of the following is equal to the average (arithmetic [#permalink]

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26 Dec 2016, 18:10
$$x^{2} + 4 + 2X + X^{2} + 4 -2X$$

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

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

C
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Re: Which of the following is equal to the average (arithmetic   [#permalink] 26 Dec 2016, 18:10
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