Question

X=2root3+2root2 : find 1/x,x+1/x and (x+1/x)^2

Answer 1

Answer:

X = 2 root 3 + 2 root 2

x = 2

Answer 2

Hi ,

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 )

Therefore ,

( x - 1/x )³ = ( - 2√3 )³

= - 24√3

I hope this helps you.