if x= 2+root3 then find the value of x2 + 1/x2

pl.. need the answer really fast................

Dear Student!

@Neha: Your friend Seema has provided the correct solution. But the correct answer would be:

   

@Seema: Good effort! Keep posting!

Cheers!!!

  • 18

 By taking LCM

x2+1/x= (2+root3)2 + 1 / (2+root3) 2 = Applying (a+b) = a +2ab+b = 4 + 4root3 + 3 + 1 / 4 + 4root3 + 3

= 8+4root3 / 7+4root3

 

  • -21

x = 2 + √3  

x2 = ( 2 + √3)2

x2 = 22 + (√3)2+ 2(2)(√3)

x2 = 4 + 3 + 4√3

x2 = 7 + 4√3

 

1/x2 =

  • -22

x = 2 + √3

 

x 2 = ( 2 + √3) 2

x 2 = 2 2 + (√3) 2 + 2(2)( √3)

x 2 = 4 + 3 + 4 √3

x 2 = 7 + 4 √3

1/x = 1/(2 + √3)

1/x 2 = 1/(2 + √3)2

1/x 2 =1/(7 + 4 √3)

1/x 2 = 1/(7 + 4 √3) * (7 - 4 √3)/(7 - 4 √3)

1/x 2 = (7 - 4 √3)/(7 + 4 √3)*(7 - 4 √3)

1/x 2 = (7 - 4 √3)/ 72 -(4 √3)2

1/x 2 = (7 - 4 √3)/ 49 - 48

1/x 2 = (7 - 4 √3) / 1

1/x 2 = (7 - 4 √3)

x 2 + 1/x 2 = (7 + 4 √3) + (7 - 4 √3)

  = 7 +   4 √3 + 7 + 4 √3

   = 14 + 8 √3

  • 12
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