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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
A. x^2
B. x^2 + 2
C. x^2 + 4
D. x^2 + 2x
E. x^2 + 4x
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Answer C.
Avg = [(x+2)^2 + (x-2)^2] / 2
Expanding and simplifying, (x^2 + 4x + 4 + x^2 - 4x + 4 ) / 2 = x^2 + 4
Avg = [(x+2)^2 + (x-2)^2] / 2
Expanding and simplifying, (x^2 + 4x + 4 + x^2 - 4x + 4 ) / 2 = x^2 + 4
cyberjadugar
Joined: 28 Mar 2012
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jsphcal
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,
Answer: C
The arithmetic mean is the sum of the elements divided by the number of elements.
The arithmetic mean is the sum of the elements divided by the number of elements.
The sum of (x+2)^2 and (x-2)^2 = 2x^2+8
Hence Average = x^2+4
Hence C
Hence Average = x^2+4
Hence C
Abhishek009
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jsphcal
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) \(x^2 + 4\)
_________________
Abhishek009
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
Posts: 17
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
Sent from my Redmi Note 3 using GMAT Club Forum mobile app
We get (0+2)^2=4 and (0-2)^2=4
Average of these two numbers =4
Only Ans (C) gives us this value
Sent from my Redmi Note 3 using GMAT Club Forum mobile app
kanusha
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Posts: 156
\(x^{2} + 4 + 2X + X^{2} + 4 -2X\)
\(\frac{2X^{2} + 8}{2}\)
\(\frac{2}{2} (X^{2} + 4)\)
C
\(\frac{2X^{2} + 8}{2}\)
\(\frac{2}{2} (X^{2} + 4)\)
C
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