Question

If x=√2 +1 then the value of x + 1/x is

Answer 1

Step-by-step explanation:

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Answer 2

Answer :

x + 1/x = 2√2

Solution :

• Given : x = √2 + 1
• To find : x + 1/x = ?

We have ;

x = √2 + 1

Thus ,

1/x = 1/(√2 + 1)

Now ,

Rationalising the denominator , we have ;

=> 1/x = (√2 - 1) / (√2 + 1)(√2 - 1)

=> 1/x = (√2 - 1) / [ (√2)² - 1² ]

=> 1/x = (√2 - 1) / (2 - 1)

=> 1/x = (√2 - 1) / 1

=> 1/x = √2 - 1

Now ,

=> x + 1/x = √2 + 1 + √2 - 1

=> x + 1/x = 2√2

Hence ,

x + 1/x = 2√2