Question

If x = 9 - 4√5, find the value of X +1/X​

Answer 1

Answer:

10 + 4√5 OR 18

Step-by-step explanation:

IF YOU MEANT (X+1)/X :

put the values of x in eq.

then rationalize it

OR

IF YOU MEANT X+(1/X) :

put the values in eq.

then rationalize 1/x

Answer 2

Answer:

18

Step-by-step explanation:

x = 9 - 4√5 → 1/x = 1/(9 - 4√5)

Rationalize the right hand side :

=> 1/x = 1/(9 - 4√5) × (9 + 4√5)/(9 + 4√5)

=> 1/x = (9 + 4√5)/(9 + 4√5)(9 - 4√5)

=> 1/x = (9 + 4√5)/(9² - (4√5)²)

=> 1/x = (9 + 4√5)/(81 - 80)

=> 1/x = 9 + 4√5

Therefore,

x + 1/x = (9 - 4√5) + (9 + 4√5)

x + 1/x = 9 + 9 = 18

Rationalization: multiplying as well as dividing by the conjugate of that number.

conjugate: let there be a number a + √b, then its conjugate is a - √b.

Here we rationalized 9 - 4√5, for which we multi. and div. by 9 + 4√5(conjugate of 9 - 4√5).