Question

If a = √2+1, then find the value of a -1/a

Answer 1

Answer:

a = √2 + 1

a - 1/a:

1/a = 1/(√2 + 1)

By rationalizing it, we get:

=> 1/(√2 + 1) × (√2 - 1)/(√2 - 1)

=> (√2 - 1)/2 - 1

=> √2 - 1

a - 1/a = √2 + 1 - √2 + 1

=> 2

_______________

Answer 2

Given :  a = √2 + 1 . …..(1)

or 1/a = 1/(√2 + 1)

By Rationalizing denominator, we have

= 1 × (√2 - 1) / [(√2 + 1) × (√2 - 1)]

= (√2 - 1) / (√2)² -  (1)²  

[We know that, (a + b) (a - b) = a² - b²]

= (√2 - 1)/(2 - 1)

= (√2 - 1)/1

= √2 - 1

1/a =  √2 - 1 ………(2)

 

Then, a - 1/a

On putting the value from eq 1 & 2 :  

= (√2 + 1) - (√2 - 1)

= √2 + 1 - √2 + 1)

= 1 + 1

a - 1/a  = 2

Hence, the value of a - 1/a is 2.

HOPE THIS ANSWER WILL HELP YOU…..

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