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# x+y=2 and xy=-3

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x+y=2 and xy=-3 [#permalink]  24 Aug 2019, 01:39
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82% (00:45) correct 17% (01:24) wrong based on 17 sessions
$$x+y=2$$ and $$xy=-3$$

 Quantity A Quantity B $$(x-y)^2$$ 16

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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[Reveal] Spoiler: OA

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Re: x+y=2 and xy=-3 [#permalink]  25 Aug 2019, 05:54
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since xy=-3 , => y=-3/x
substitute y's value in x+y=2
we get quad. eq. x^2 - 2x -3 = 0
sol. gives x=3 or x=-1
which gives y=-1 if x=3 or y=3 if x=-1
put values in the expression to get an answer that's 16
which is equal to Quantity B
hence answer is C
Intern
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Re: x+y=2 and xy=-3 [#permalink]  22 Dec 2019, 06:51
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Here xy = -3, Let, x = -1 & y = 3. Then, xy = -1 X 3 = -3, and x + y = -1 + 3 = 2.
Then square of (x-y) = square of (-1-3) = 16.
Then Ans is C.
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Re: x+y=2 and xy=-3 [#permalink]  24 Dec 2019, 04:22
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(x-y)^2 = (x+y)^2 - 4xy
= (2)^2 -4(-3)
= 4+ 12
= 16

A = B = 16

Hence, C is the Answer.
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Re: x+y=2 and xy=-3 [#permalink]  24 Dec 2019, 08:20
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$$(x+y)^2 - (x-y)^2 = 4xy$$
$$4 - 4(-3) = (x-y)^2$$
$$(x-y)^2 = 16$$

OA,C
Carcass wrote:
$$x+y=2$$ and $$xy=-3$$

 Quantity A Quantity B $$(x-y)^2$$ 16

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation

_________________

If you like my solution, do give kudos!

Re: x+y=2 and xy=-3   [#permalink] 24 Dec 2019, 08:20
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