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

Question

A. –2 
B. –1
C. 0
D. 1
E. 2

AnisMURR · Accepted Answer

hello,

Here is the answer, hope it is clear

Shrivathsan · Answer

(x+y)^2 = x^2+y^2+2xy
4=2+2xy
xy=1
D

chetan2u · Answer

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

msk0657 · Answer

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.

gauravk · Answer

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

Akuthiala · Answer

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

Ndkms · Answer

Nice! Simple question.... How is it possible to see this under 2 min? LOL!?

dave13 · Answer

Guys what is the relationship between x + y = 2 and x^2 + y^2 = 2 in question itself

?

pushpitkc · Answer

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!

MSGmat1 · Answer

Two equations are given to form a basic algebra equation.

(x+y)^2= x^2+y^2+2xy
Hence value of xy=1

Sent from my iPhone using GMAT Club Forum

dave13 · Answer

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

pushpitkc · Answer

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!

dave13 · Answer

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!

pushpitkc · Answer

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.

Kinshook · Answer

(x+y)^2= x^2+y^2+2xy
4 = 2 + 2xy
xy = 1

IMO D

Posted from my mobile device

PranavVyas · Answer

x+y=2
x^2+y^2=2

replace values of xy from options , that give answer =2 as per equation.

x+y=2 => 1+1=2
x^2+y^2 =>1^2+1^2=2
xy =>1*1=2

So, 1 is the answer
 Option D

MrMaxMan · Answer

If x and y were any integer other than 1, then the sum of the two squares would not be 2. To verify that both are 1 even more, we can see that x+y=2.

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 ?

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