Question

if x=3+2√2,then find the value of √x-√1/√x​

Answer 1

Answer:

2√2

Step-by-step explanation:

Given----> x = 3 + 2√2

To find-----> Value of ( √x - 1 / √x )

Solution----> ATQ,

x = 3 + 2√2

= 1 + 2 + 2√2

= ( 1 )² + ( √2 )² + 2 ( 1 ) ( √2 )

We know that,

( a + b )² = a² + b² + 2ab , applying it we get ,

= ( 1 + √2 )²

Now , √x = √( 1 + √2 )²

= ( 1 + √2 )

Now,

1 / √x = 1 / ( 1 + √2 )

Multiplying in numerator and denominator by conjugate of denominator by ( √2 - 1 ) , we get,

=> 1 / √x = ( √2 - 1 ) / ( √2 + 1 ) ( √2 - 1 )

We know that,

( a² - b² ) = ( a + b ) ( a - b ) , applying it in denominator , we get,

= ( √2 - 1 ) / { ( √2 )² - ( 1 )² }

= ( √2 - 1 ) / ( 2 - 1 )

= ( √2 - 1 ) / 1

=> 1 / √x = ( √2 - 1 )

Now, √x - 1 / √x = ( 1 + √2 ) + ( √2 - 1 )

= 2√2