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# If the average of m and (x + y)^2 = x^2 + y^2 , what

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If the average of m and (x + y)^2 = x^2 + y^2 , what [#permalink]  27 Aug 2018, 09:37
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Question Stats:

89% (01:03) correct 10% (01:36) wrong based on 28 sessions
If the average of m and $$(x + y)^2 = x^2 + y^2$$ , what is the value of m ?

A. x-y

B. x+y

C. (x-y)(x+y)

D. $$(x-y)^2$$

E. $$(x+y)^2$$
[Reveal] Spoiler: OA

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Re: If the average of m and (x + y)^2 = x^2 + y^2 , what [#permalink]  27 Aug 2018, 10:43
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Expert's post
Carcass wrote:
If the average of m and $$(x + y)^2 = x^2 + y^2$$ , what is the value of m ?

A. x-y

B. x+y

C. (x-y)(x+y)

D. $$(x-y)^2$$

E. $$(x+y)^2$$

The average of m and (x + y)² = x² + y²
So: [m + (x + y)²]/2 = x² + y²
Multiply both sides by 2 to get: m + (x + y)² = 2x² + 2y²
Expand left side to get: m + x² + 2xy + y² = 2x² + 2y²
Subtract x² from both sides to get: m + 2xy + y² = x² + 2y²
Subtract y² from both sides to get: m + 2xy = x² + y²
Subtract 2xy from both sides to get: m = x² - 2xy + y²
Factor right side to get: m = (x - y)²

Cheers,
Brent
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Re: If the average of m and (x + y)^2 = x^2 + y^2 , what   [#permalink] 27 Aug 2018, 10:43
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# If the average of m and (x + y)^2 = x^2 + y^2 , what

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