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

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If the average of m and (x + y)^2 = x^2 + y^2 , what is the value of m  [#permalink]

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27 Aug 2018, 10:37
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Question Stats:

87% (00:59) correct 13% (01:22) wrong based on 29 sessions

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

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Joined: 25 Jan 2013
Posts: 20
Concentration: Marketing, Strategy
GPA: 3.64
If the average of m and (x + y)^2 = x^2 + y^2 , what is the value of m  [#permalink]

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27 Aug 2018, 10:55
1
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. $$(x+y)^2$$

$$\frac{m+(x+y)^2}{2}$$ = $$x^2+y^2$$

=>m+$$(x+y)^2$$= $$2x^2+2y^2$$
=>m = $$2x^2+2y^2 - x^2-2xy-y^2$$
=> m = $$(x-y)^2$$

IMO, D
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Re: If the average of m and (x + y)^2 = x^2 + y^2 , what is the value of m  [#permalink]

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27 Aug 2018, 10:56
1
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. $$(x+y)^2$$

$$\frac{m + x^2 + 2xy + y^2}{2} = x^2 + y^2$$

Or, $$m + x^2 + y^2 + 2xy = 2x^2 + 2y^2$$

Or, $$m = x^2 + y^2 - 2xy$$

Or, $$m = ( x - y )^2$$, Answer must be (D)
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Re: If the average of m and (x + y)^2 = x^2 + y^2 , what is the value of m   [#permalink] 27 Aug 2018, 10:56
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