Question

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

Answer 1

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