Question

If x= 7+ 4 root 3 then find x+1/x

Answer 1

x+1/x=7+4√3 + 1/7+4√3
7+4√3+7-4√3/1 .... (rationalizing the denominator)
14
answer is 14

Answer 2

Hi ,

x = 7 + 4√3 ----( 1 )

1/x = 1 / ( 7 + 4√3 )

Rationalize the denominator,

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

= ( 7 - 4√3 ) / [ 7² - ( 4√3 )² ]

= ( 7 - 4√3 ) / [ 49 - 48 ]

1/x = 7 - 4√3 ----( 2 )

Therefore ,

x + 1/x = ( 1 ) + ( 2 )

= 7 + 4√3 + 7 - 4√3

= 14

I hope this helps you.

:)