Question

if x =2+✓3 find the value of x+1/x^2

Answer 1

Hi ,

I think there is an error in the question .



It is given that ,

x = 2 + √3 ---( 1 )

1/x = 1/( 2 + √3 )

= ( 2 - √3 )/[ ( 2 + √3 )( 2 - √3 )

= ( 2 - √3 )/ [ 2² - ( √3 )² ]

= ( 2 - √3 )/ ( 4 - 3 )

1/x = 2 - √3 ---( 2 )

Now ,

value of x² + 1/x²


= ( x + 1/x )² - 2

= [ 2 + √3 + 2 - √3 ]² - 2

= 4² - 2

= 16 - 2

= 14

I hope this helps you.

: )

Answer 2

According to the question,

x = 2+√3

=====================

1/x = 1/(2+√3)

By rationalization,

=> 1/x = (2-√3)/[(2+√3)(2-√3)]

=> 1/x = (2-√3)/[(2²-√3²)

=> 1/x = (2-√3)/(4-3)

=> 1/x = (2-√3)/1 = 2-√3

=> 1/x² = (2-√3)²

=> 1/x² = 4+3-4√3


__________________________

Now,


x + 1/x²

=> 2+√3 + 4 +3 -4√3

=> 9 -3√3


I hope this will help you


-by ABHAY