Question

Given that a=√2 + √3 , find the value of a-1/a

Answer 1

a = √2 + √3

=> 1/a = 1 / ( √2 + √3 )

rationalizing ,

=> 1/a = { √2 - √3 } / { ( √2 + √3 ) ( √2 - √3 )

=> 1/a = ( √2 - √3 ) / { (√2)² - (√3)² }

=> 1/a = ( √2 - √3 ) / (-1)

=> -1/a = √2 - √3.............. (1)

now , a - 1/a = √2 + √3 + √2 - √3 ........... ( from (1))

=> a - 1/a = 2√2

Answer 2

Step-by-step explanation:

a = √2 + √3

Therefore

1/a = 1/(√2 + √3)

Since it Has Root in denominator.

Therefore we have to Rationalise it

To remove Root

We have to multiply and divide by the conjugate ie. √2 - √3

1 = 1 × √2 - √3

---- --------- -------------

a √2 + √3 √2 - √3

1/a = (√2 - √3) / (2 - 3) = (√2 - √3) / -1

1/a = √3 - √2

Putting the values

a - 1/a = √2 + √3 - ( √3 - √2)

= √2 + √3 - √3 + √2 = 2√2

Therefore Value of a - 1/a is 2√2