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# x2−2xy+y2=0 and xy = 9.

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Manager
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x2−2xy+y2=0 and xy = 9. [#permalink]  11 Sep 2018, 12:56
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Question Stats:

64% (00:44) correct 35% (01:01) wrong based on 28 sessions
$$x^2−2xy+y^2=0$$ and $$xy=9$$

 Quantity A Quantity B y 3

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

Official answer says D (Cannot be determined) but I strongly believe it is C (Quantities are equal)
[Reveal] Spoiler: OA

Last edited by Carcass on 11 Sep 2018, 14:43, edited 1 time in total.
Edited by Carcass
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Re: x2−2xy+y2=0 and xy = 9. [#permalink]  11 Sep 2018, 17:57
1
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Expert's post
This is one of the questions you need to pay attention.

Given: $$x^2−2xy+y^2=0$$ or $$(x-y)^2=0$$ or $$x=y$$

Also given that $$xy=9$$, substituting value of x in terms of y or $$y^2=9$$ Here y can have 2 values 3 and -3.

Hence D is correct
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Sandy
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Manager
Joined: 27 Feb 2017
Posts: 188
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Kudos [?]: 76 [0], given: 15

Re: x2−2xy+y2=0 and xy = 9. [#permalink]  11 Sep 2018, 18:04
sandy wrote:
This is one of the questions you need to pay attention.

Given: $$x^2−2xy+y^2=0$$ or $$(x-y)^2=0$$ or $$x=y$$

Also given that $$xy=9$$, substituting value of x in terms of y or $$y^2=9$$ Here y can have 2 values 3 and -3.

Hence D is correct

OHH!! The minus sign, I totally ignored that. Thanks, Sandy! I got confused with the explanation because it stated the combination of y= 9 or 1 as the reasoning, which did not fall in line with the given quadratic equation.
Senior Manager
Joined: 10 Feb 2020
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Kudos [?]: 81 [0], given: 222

Re: x2−2xy+y2=0 and xy = 9. [#permalink]  10 Jun 2020, 16:59
sandy wrote:
This is one of the questions you need to pay attention.

Given: $$x^2−2xy+y^2=0$$ or $$(x-y)^2=0$$ or $$x=y$$

Also given that $$xy=9$$, substituting value of x in terms of y or $$y^2=9$$ Here y can have 2 values 3 and -3.

Hence D is correct

How do you substitute?
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Manager
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Re: x2−2xy+y2=0 and xy = 9. [#permalink]  10 Jun 2020, 21:25
2
KUDOS
Farina wrote:
sandy wrote:
This is one of the questions you need to pay attention.

Given: $$x^2−2xy+y^2=0$$ or $$(x-y)^2=0$$ or $$x=y$$

Also given that $$xy=9$$, substituting value of x in terms of y or $$y^2=9$$ Here y can have 2 values 3 and -3.

Hence D is correct

How do you substitute?

x = y
xy = 9
y^2 = 9
Thus, y can be +3 or -3.
Re: x2−2xy+y2=0 and xy = 9.   [#permalink] 10 Jun 2020, 21:25
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# x2−2xy+y2=0 and xy = 9.

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