if x= root 3+1 / root 3-1 and y = root 3 -1 / root 3+1 find the value of x square + y square + xy​

2 thoughts on “if x= root 3+1 / root 3-1 and y = root 3 -1 / root 3+1 find the value of x square + y square + xy​”

1. Answer:

   Step-by-step explanation:e have, given that x,y are the roots of the equation x

   2
   

   +bx+1=0
   

   ∴x+y=−b and xy=1
   

   
   

   Now,
   x+b
   

   1
   

   ​

   +

   (y+b)
   

   1
   

   ​

   =

   (x+b)(y+b)
   

   y+b+x+b
   

   ​

   
   

   =

   xy+b(x+y)+b

   2
   

   (x+y)+2b
   

   ​

   
   

   =

   1+b(−b)+b

   2
   

   −b+2b
   

   ​

   
   

   =

   1−b

   2
   

   +b

   2
   

   b
   

   ​

   =b

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2. Step-by-step explanation:

   x= √3+1/√3-1

   y= √3-1/√3+1

   Rationalize

   x= 2+√3

   y= 2-√3

   x²+y²+xy = 7+4√3+7-4√3+1 = 15

   Answer is 15

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