Question

If x= 4-√5 then value of x+ 1/x is equal to

Answer 1

Answer:

x + 1/x = (48 - 10√5) / 11

Solution:

• Given : x = 4 - √5
• To find : x + 1/x = ?

We have ,

x = 4 - √5

Thus,

1/x = 1/(4 - √5)

Now,

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

=> 1/x = (4 + √5)/(4 - √5)(4 + √5)

=> 1/x = (4 + √5)/[ 4² - (√5)² ]

=> 1/x = (4 + √5) / (16 - 5)

=> 1/x = (4 + √5)/11

Thus,

x + 1/x = (4 - √5) + (4 + √5) / 11

= [ 11(4 - √5) + (4 + √5) ] / 11

= ( 44 - 11√5 + 4 + √5 ) / 11

= (48 - 10√5) / 11

Hence,

x + 1/x = (48 - 10√5) / 11