Question

if x=2+√3 ,then (x+1/x) equals to​

Answer 1

Step-by-step explanation:

x = 2 - √3--( 1 )

1/x = 1/( 2 - √3 )

= ( 2 + √3 ) / [ ( 2 - √3 )(2 + √3 ) ]

= ( 2 + √3 ) / [ 2² - ( √3 )² ]

= ( 2 + √3 ) / ( 4 - 3 )

= 2 + √3 ----( 2 )

x - 1/x

= 2 - √3 - ( 2 + √3 )

= 2 - √3 - 2 - √3

= - 2√3 ---( 3 )

so,

( x - 1/x )³ = ( - 2√3 )³

= - 24√3

Answer 2

x = 2 + √3

1/x = 1/2 + √3 × (2 - √3/2 - √3)

1/x = 2 - √3/4 - 3

1/x = 2 - √3

x - 1/x = 2 + √3 + 2 - √3

x - 1/x = 4