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WE:**Business Development (Energy and Utilities)**

If a = (x + y)2 and b = x2 + y2 and xy > 0, which of the fol
[#permalink]
23 Jun 2018, 12:40

1

Expert Reply

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Question Stats:

If \(a = (x + y)^2\) and \(b = x^2 + y^2\) and \(xy > 0\), which of the following must be true?

Indicate all such statements.

A. a = b

B. a > b

C. a is positive

_________________

Indicate all such statements.

A. a = b

B. a > b

C. a is positive

_________________

Sandy

If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Re: If a = (x + y)2 and b = x2 + y2 and xy > 0, which of the fol
[#permalink]
24 Jun 2018, 06:53

2

sandy wrote:

If \(a = (x + y)^2\) and \(b = x^2 + y^2\) and \(xy > 0\), which of the following must be true?

Indicate all such statements.

A. a = b

B. a > b

C. a is positive

Indicate all such statements.

A. a = b

B. a > b

C. a is positive

We are given that xy > 0 , i.e. both xy are -ve or both +ve.

A. When we expand a and b.

finally we get 2xy = 0 , and we know that 2xy is not equal to 0...eliminate.

B. 2xy > 0 , as xy>0 , then 2xy must be greater than 0 ... yes

C. a is +ve , when we take x and y both -ve or both +ve , finally we get a has +ve itself...Yes

B and C.

Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4806**

WE:**Business Development (Energy and Utilities)**

Re: If a = (x + y)2 and b = x2 + y2 and xy > 0, which of the fol
[#permalink]
28 Jul 2018, 16:15

Expert Reply

Explanation

Distribute for a: \(a = (x + y)^2 = x^2 + 2xy + y^2\). Since \(b = x^2 + y^2\), a and b are the same except for the “extra” 2xy in a.

Since xy is positive, a is greater than b. The 1st statement is false and the 2nd statement is true.

Each term in the sum for a is positive: xy is given as positive, and \(x^2\) and \(y^2\) are definitely positive, as they are squared and not equal to zero. Therefore, \(a = x^2 + 2xy + y^2\) is positive. The 3rd statement is true.

_________________

Sandy

If you found this post useful, please let me know by pressing the Kudos Button

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Distribute for a: \(a = (x + y)^2 = x^2 + 2xy + y^2\). Since \(b = x^2 + y^2\), a and b are the same except for the “extra” 2xy in a.

Since xy is positive, a is greater than b. The 1st statement is false and the 2nd statement is true.

Each term in the sum for a is positive: xy is given as positive, and \(x^2\) and \(y^2\) are definitely positive, as they are squared and not equal to zero. Therefore, \(a = x^2 + 2xy + y^2\) is positive. The 3rd statement is true.

_________________

If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Re: If a = (x + y)2 and b = x2 + y2 and xy > 0, which of the fol
[#permalink]
08 May 2020, 04:58

This one is easier than it looks!

x^2 + 2xy + y^2 vs. x^2 +y^2

xy>0 and anything squared (on the GRE) is ALWAYS ALWAYS ALWAYS positive.

Past these rules it's basic logic.

x^2 + 2xy + y^2 vs. x^2 +y^2

xy>0 and anything squared (on the GRE) is ALWAYS ALWAYS ALWAYS positive.

Past these rules it's basic logic.

Re: If a = (x + y)2 and b = x2 + y2 and xy > 0, which of the fol
[#permalink]
07 May 2023, 10:15

Hello from the GRE Prep Club BumpBot!

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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