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If a = (x + y)2 and b = x2 + y2 and xy > 0, which of the fol
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23 Jun 2018, 12:40
23 Jun 2018, 12:40
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78% (00:56) correct
21% (01:20) wrong based on 104 sessions
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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
Re: If a = (x + y)2 and b = x2 + y2 and xy > 0, which of the fol
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24 Jun 2018, 06:53
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.
Re: If a = (x + y)2 and b = x2 + y2 and xy > 0, which of the fol
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28 Jul 2018, 16:15
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.
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.
