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If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?

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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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New post 26 Sep 2016, 04:01
12
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A
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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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New post 26 Sep 2016, 04:11
2
1
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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New post 26 Sep 2016, 04:15
1
1
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=4-2=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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New post 27 Sep 2016, 04:09
1
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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New post 27 Sep 2016, 04:14
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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New post 27 Sep 2016, 14:22
1
x+y = 2 or x = 2-y

x^2+Y^2=2
(2-Y)^2+Y^2=2
y^2-2Y+1=0
Y=1

X=2-y
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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New post 31 Oct 2016, 11:34
2
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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New post 10 Jan 2017, 12:18
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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New post 15 Mar 2018, 09:41
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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New post 15 Mar 2018, 10:07
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 dave13

In 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 \((x+y)^2 | (x-y)^2 | x^2 - y^2\)

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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New post 15 Mar 2018, 10:10
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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New post 15 Mar 2018, 10:31
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 dave13

In 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 \((x+y)^2 | (x-y)^2 | x^2 - y^2\)

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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New post 15 Mar 2018, 11:04
1
Hey dave13

We 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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New post 16 Mar 2018, 11:05
pushpitkc wrote:
Hey dave13

We 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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New post 16 Mar 2018, 11:46
2
dave13 wrote:
pushpitkc wrote:
Hey dave13

We 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 dave13

So 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 = 4-2 = 2

Therefore, xy = \(\frac{2}{2} = 1\)

Hope it is clear now.
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