Question

if x = 3+√8 then find x+1/x​

Answer 1

Answer:

given, x= 3+√8

now, x+1/x

= (X2+1)/x

= {(3+√8)2+1}/(3+√8)

={9+6√8+8+1}/(3+√8)

= (18+6√8)/(3+√8)

= 6(3+√8)/(3+√8)

=6

the answer is 6

Answer 2

x + 1/x = 6

Step-by-step explanation:

We are given that x = 3 + √8. Therefore,

→ 1/x = 1/(3 + √8)

→ 1/x = [1(3 - √8)/(3 + √8)(3 - √8)]

→ 1/x = [(3 - √8)/(3² - (√8)²)] --- [(a + b)(a - b) = a² - b²]

→ 1/x = [(3 - √8)/(9 - 8)]

→ 1/x = [(3 - √8)/(1)]

→ 1/x = 3 - √8

Therefore, let's find the value of x + 1/x.

→ x + 1/x = (3 + √8) + (3 - √8)

→ x + 1/x = 6

Hence, the value of x + 1/x is 6.

Concepts used:

1. Here, the concept of rationalisation is used. With this method, we had removed the radical sign at denominator (√8). This method also makes our calculations easier.
2. When we are rationalising the denominator, we are using the algebraic identity: (a + b)(a - b) = a² - b².