Question

ifx3+√8show that x2+1/x2=34

Answer 1

Hi ,

It is given that ,

x = 3 + √8 ---( 1 )

1/x = 1/( 3 + √8 )

= ( 3 - √8 ) /[ ( 3 + √8 )(3 - √8 )]

= ( 3 - √8 )/[ 3² - ( √8 )² ]

= ( 3 - √8 ) / ( 9 - 8 )

1/x = 3 - √8 -----( 2 )

Add equations ( 1 ) and ( 2 ) we get ,

x + 1/x = 3 + √8 + 3 - √8

x + 1/x = 6

Do the Square of both sides of above

equation ,

( x + 1/x )² = 6²

x ² + 1/x² + 2 × x × 1/x = 36

x² + 1/x² + 2 = 36

Therefore ,

x² + 1/x² = 36 - 2 = 34

I hope this helps you.

: )