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If x - y = sqrt(3) and x + y = 2, then xy = ?

 Jun 27, 2022
 #1
avatar+124509 
+1

x - y = sqrt (3)

x + y = 2              add these

 

2x  = 2 + sqrt (3)

 

x =   [ 2 + sqrt (3) ]  /2

 

y =     2 - x

 

y =  2 - [2 + sqrt (3) ] / 2  = ( 4 - [2 + sqrt 3] )  / 2  =     [ 2 - sqrt (3)] / 2

 

xy  =   [ 2 + sqrt (3) ]  /  2   *    [2 -sqrt (3) ] / 2  =     (4 - 3) / 4 =   1/4

 

 

cool cool cool

 Jun 27, 2022
 #2
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+2

Square the first equation,

\(\displaystyle x^{2}+y^{2}-2xy=3,\dots(1) \)

Square the  second equation,

\(\displaystyle x^{2}+y^{2}+2xy =4,\dots(2)\)

Subtract (1) from (2),

\(\displaystyle 4xy=1, \\ xy=1/4.\)

 Jun 28, 2022

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