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# For all numbers a and b, let a#b = (a + b)^2 – 2ab. Which of the follo

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Math Expert
Joined: 02 Sep 2009
Posts: 44645
For all numbers a and b, let a#b = (a + b)^2 – 2ab. Which of the follo [#permalink]

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09 Apr 2018, 02:39
00:00

Difficulty:

45% (medium)

Question Stats:

27% (01:03) correct 73% (01:40) wrong based on 14 sessions

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For all numbers a and b, let a#b = (a + b)^2 – 2ab. Which of the following must be true?

I. x#y = y#x
II. (x#y)#z = (z#x)#y
III. (x + y)#(x – y) = 2(x#y)

A. I
B. II only
C. III only
D. I and III only
E. II and III only
[Reveal] Spoiler: OA

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Joined: 18 Aug 2016
Posts: 631
Re: For all numbers a and b, let a#b = (a + b)^2 – 2ab. Which of the follo [#permalink]

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09 Apr 2018, 03:03
Bunuel wrote:
For all numbers a and b, let a#b = (a + b)^2 – 2ab. Which of the following must be true?

I. x#y = y#x
II. (x#y)#z = (z#x)#y
III. (x + y)#(x – y) = 2(x#y)

A. I
B. II only
C. III only
D. I and III only
E. II and III only

a#b = (a + b)^2 – 2ab
a#b = $$a^2 + b^2$$

I
x#y = $$x^2 + y^2$$ = y#x...Stands

II
(x#y)#z = $$(x^2+y^2)^2 + z^2$$
(z#x)#y = $$(z^2+x^2)^2 + y^2$$
Not equal

III
(x + y)#(x – y) = 2(x#y)
$$(x+y)^2 + (x-y)^2 = 2 (x^2 + y^2)$$ = 2 (x#y)

I and III
D
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Re: For all numbers a and b, let a#b = (a + b)^2 – 2ab. Which of the follo   [#permalink] 09 Apr 2018, 03:03
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