Find the value of root x-1/root x if x= 2+root 3

1.	Find the value of root x-1/root x if x= 2+root 3
Answer» ANSWER : √x - 1/√x = √6 SOLUTION : Given : x = 2 + √3 To FIND : √x - 1/√x = ? We have , x = 2 + √3 Thus , => 1/x = 1/(2 + √3) => 1/x = (2 - √3) / (2 + √3)•(2 - √3) => 1/x = (2 - √3) / [ 2² - (√3)² ] => 1/x = (2 - √3) / (4 - 3) => 1/x = (2 - √3) / 1 => 1/x = 2 - √3 Now , => (√x - 1/√x)² = (√x)² - 2•√x•(1/√x)+(1/√x)² => (√x - 1/√x)² = x + 2 + 1/x => (√x - 1/√x)² = 2 + √3 + 2 + 2 - √3 => (√x - 1/√x)² = 6 => (√x - 1/√x) = √6 Hence , √x - 1/√x = √6

Answer»

ANSWER :

√x - 1/√x = √6

Given : x = 2 + √3

To FIND : √x - 1/√x = ?

We have , x = 2 + √3

Thus ,

=> 1/x = 1/(2 + √3)

=> 1/x = (2 - √3) / (2 + √3)•(2 - √3)

=> 1/x = (2 - √3) / [ 2² - (√3)² ]

=> 1/x = (2 - √3) / (4 - 3)

=> 1/x = (2 - √3) / 1

=> 1/x = 2 - √3

Now ,

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

=> (√x - 1/√x)² = x + 2 + 1/x

=> (√x - 1/√x)² = 2 + √3 + 2 + 2 - √3

=> (√x - 1/√x)² = 6

=> (√x - 1/√x) = √6