Question

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

Answer 1

Answer:

The value of  \sqrt x - \frac{1}{\sqrt x} is 2.

Step-by-step explanation:

Given:

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

Solution:

x = 3 + 2 \sqrt2

= 1 + 2\sqrt2 + 2

=(1 + \sqrt2)2

\sqrt x = 1+ \sqrt2

\sqrt x - \frac{1}{\sqrt x} = (1 + \sqrt2) - \frac{1}{(1 + \sqrt2)}

After simplification, we get  

\sqrt x - \frac{1}{\sqrt x} = 2 \frac{(1 + \sqrt2)}{(1 + \sqrt2)}

\sqrt x - \frac{1}{\sqrt x} = 2

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Answer 2

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