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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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26 Sep 2016, 05:01
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Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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26 Sep 2016, 05:11
Bunuel wrote: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?
A. –2 B. –1 C. 0 D. 1 E. 2 (x+y)^2 = x^2+y^2+2xy 4=2+2xy xy=1 D
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Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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26 Sep 2016, 05:15
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Bunuel wrote: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?
A. –2 B. –1 C. 0 D. 1 E. 2 It is based on algebraic formula.. (X+y)^2=x^2+y^2+2xy.. Substitute the values given.. 2^2=2+2xy... 2xy=42=2.... xy=1 D
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Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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27 Sep 2016, 05:09
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Bunuel wrote: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?
A. –2 B. –1 C. 0 D. 1 E. 2 x^2 + y^2 = 2  Given we can write the above equation as \((x+y)^2\)  2xy = 2 \((2)^2\)2xy = 2 => 4  2xy = 2 => 2xy = 2 => xy = 1. Option D.



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Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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27 Sep 2016, 05:14
Given (x+Y) = 2 and X^2 + Y^2 = 2 (x+Y) = 2 Squaring both sides.
X^2 + Y^2 + 2xy = 4
2 + 2xy = 4
Solving for xy = 1
Option D



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Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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27 Sep 2016, 15:22
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x+y = 2 or x = 2y
x^2+Y^2=2 (2Y)^2+Y^2=2 y^22Y+1=0 Y=1
X=2y X=1
Ans 1 D



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Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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31 Oct 2016, 12:34
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hello, Here is the answer, hope it is clear
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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10 Jan 2017, 13:18
Shrivathsan wrote: Bunuel wrote: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?
A. –2 B. –1 C. 0 D. 1 E. 2 (x+y)^2 = x^2+y^2+2xy 4=2+2xy xy=1 D Nice! Simple question.... How is it possible to see this under 2 min? LOL!?



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Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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15 Mar 2018, 10:41
Bunuel wrote: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?
A. –2 B. –1 C. 0 D. 1 E. 2 Guys what is the relationship between x + y = 2 and x^2 + y^2 = 2 in question itself ?



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Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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15 Mar 2018, 11:07
dave13 wrote: Bunuel wrote: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?
A. –2 B. –1 C. 0 D. 1 E. 2 Guys what is the relationship between x + y = 2 and x^2 + y^2 = 2 in question itself ? Hi dave13In the question itself, there is no relationship between the 2 equations except that they are talking about the same variable x and y. In questions like these, we are basically given two simultaneous linear equations and are excepted to find the value of x and y solving these equations. Some basic formulae you need to remember are \((x+y)^2  (xy)^2  x^2  y^2\) Hope this helps!
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Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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15 Mar 2018, 11:10
Two equations are given to form a basic algebra equation.
(x+y)^2= x^2+y^2+2xy Hence value of xy=1
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Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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15 Mar 2018, 11:31
pushpitkc wrote: dave13 wrote: Bunuel wrote: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?
A. –2 B. –1 C. 0 D. 1 E. 2 Guys what is the relationship between x + y = 2 and x^2 + y^2 = 2 in question itself ? Hi dave13In the question itself, there is no relationship between the 2 equations except that they are talking about the same variable x and y. In questions like these, we are basically given two simultaneous linear equations and are excepted to find the value of x and y solving these equations. Some basic formulae you need to remember are \((x+y)^2  (xy)^2  x^2  y^2\) Hope this helps! Hello pushpitkc thanks for your reply ok i understand how from this x^2 + y^2 = 2, we do this (x+y) (x+y) = x^2+xy+yx+y^2 = x^2+y^2+2xy = 2 ok now what ? and what am i to do with x + y = 2 ? there are no roots, powers etc here



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Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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15 Mar 2018, 12:04
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Hey dave13We are given in the question stem that \(x+y = 2\) and \(x^2 + y^2 = 2\) After you have figured that \((x+y)^2 = x^2 + y^2 + 2xy\) Substituting these values, we get\(2^2 = 2 + 2xy\) > \(4  2 = 2xy\) > \(xy = \frac{2}{2} = 1\)(Option D) Hope this helps!
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Re: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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16 Mar 2018, 12:05
pushpitkc wrote: Hey dave13We are given in the question stem that \(x+y = 2\) and \(x^2 + y^2 = 2\) After you have figured that \((x+y)^2 = x^2 + y^2 + 2xy\) Substituting these values, we ge t\(2^2 = 2 + 2xy\) > \(4  2 = 2xy\) > \(xy = \frac{2}{2} = 1\)(Option D) Hope this helps! pushpitkc many thanks for explanation. yes it helps just partially ok from this \(x^2 + y^2 = 2\) we got this \(x^2 + y^2 + 2xy =2\) ok I understand this part so far now you say we substitute values  which values are you talking about? and in which equation do you substitute ? how do you get this \(2^2 = 2 + 2xy\) also how do you get in it \(2^2\) I would appreciate your detailed explanation for dummies thanks!



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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ? [#permalink]
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16 Mar 2018, 12:46
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dave13 wrote: pushpitkc wrote: Hey dave13We are given in the question stem that \(x+y = 2\) and \(x^2 + y^2 = 2\) After you have figured that \((x+y)^2 = x^2 + y^2 + 2xy\) Substituting these values, we ge t\(2^2 = 2 + 2xy\) > \(4  2 = 2xy\) > \(xy = \frac{2}{2} = 1\)(Option D) Hope this helps! pushpitkc many thanks for explanation. yes it helps just partially ok from this \(x^2 + y^2 = 2\) we got this \(x^2 + y^2 + 2xy =2\) ok I understand this part so far now you say we substitute values  which values are you talking about? and in which equation do you substitute ? how do you get this \(2^2 = 2 + 2xy\) also how do you get in it \(2^2\) I would appreciate your detailed explanation for dummies thanks! Hey dave13So we have an equation \((x+y)^2 = x^2 + y^2 + 2xy\) > (1) The question stem has given us the following details: \(x+y = 2\) \(x^2 + y^2 = 2\) > (2) Because \(x+y = 2\), value of \((x+y)^2 = 2^2 = 4\) > (3) Substituting values from (2) and (3) in equation (1) \((x+y)^2\) = \(x^2 + y^2\)\(+ 2xy\) 4 = 2 + 2xy 2xy = 42 = 2 Therefore, xy = \(\frac{2}{2} = 1\) Hope it is clear now.
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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?
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