Question

X=(7 +4 root 3 ) then x+1/x=

Answer 1

Answer :

x + 1/x = 14

Solution :

• Given : x = 7 + 4√3
• To find : x + 1/x

We have ;

x = 7 + 4√3

Thus ,

1/x = 1/(7 + 4√3)

Now ,

Rationalising the denominator of the term in RHS , we get ;

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

=> 1/x = (7 - 4√3) / [ 7² - (4√3)² ]

=> 1/x = (7 - 4√3) / (49 - 48)

=> 1/x = (7 - 4√3) / 1

=> 1/x = 7 - 4√3

Now ,

=> x + 1/x = 7 + 4√3 + 7 - 4√3

=> x + 1/x = 14

Hence ,

x + 1/x = 14

Answer 2

Answer:

Step-by-step explanation:

1/x = (7 - 4√3) / (7 + 4√3)(7 - 4√3)

= 1/x = (7 - 4√3) / [ 7² - (4√3)² ]

= 1/x = (7 - 4√3) / (49 - 48)

= 1/x = (7 - 4√3) / 1

= 1/x = 7 - 4√3

Therefore  

= x + 1/x = 7 + 4√3 + 7 - 4√3

= x + 1/x = 14

x + 1/x = 14