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If x #y = (x + y)(x - y) for all real numbers, then which of the follo
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09 Mar 2022, 04:00
09 Mar 2022, 04:00
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If x #y = (x + y)(x - y) for all real numbers, then which of the following must be true?
I. x #y = y #x
II. x #0 = 0 #x = x^2
III. x #-y = x #y
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
I. x #y = y #x
II. x #0 = 0 #x = x^2
III. x #-y = x #y
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
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Re: If x #y = (x + y)(x - y) for all real numbers, then which of the follo
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25 Mar 2022, 05:51
25 Mar 2022, 05:51
1
Carcass wrote:
If x #y = (x + y)(x - y) for all real numbers, then which of the following must be true?
I. x #y = y #x
II. x #0 = 0 #x = x^2
III. x #-y = x #y
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
I. x #y = y #x
II. x #0 = 0 #x = x^2
III. x #-y = x #y
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
I. x # y = y # x
x # y = (x + y)(x - y) = \(x^2 - y^2\)
y # x = (y + x)(y - x) = \(y^2 - x^2\)
Not true always
II. x # 0 = 0 # x = \(x^2\)
x # 0 = (x + 0)(x - 0) = \(x^2\)
0 # x = (0 + x)(0 - x) = \(-x^2\)
III. x # -y = x # y
x # -y = [x + (-y)][x - (-y)] = [x - y][x + y] = \(x^2 - y^2\)
x # y = (x - y)(x + y) = \(x^2 - y^2\)
Hence, option C
gmatclubot
Re: If x #y = (x + y)(x - y) for all real numbers, then which of the follo [#permalink]
25 Mar 2022, 05:51
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