Question

If A= 5+2√6 ,so find that value of √A+ 1/√A .

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Answer 1

Step-by-step explanation:

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Answer 2

Answer:

√A + 1/√A = 2√3

Solution:

Given: A = 5 + 2√6

To find : √A + 1/√A

We have ,

=> A = 5 + 2√6

=> A = 3 + 2 + 2√6

=> A = 3 + 2√6 + 2

=> A = (√3)² + 2•√3•√2 + (√2)²

=> A = (√3 + √2)²

=> √A = √3 + √2 --------(1)

Now,

=> √A = √3 + √2

=> 1/√A = 1/(√3 + √2)

Rationalising the denominator of the term in RHS , we have ;

=> 1/√A = (√3 - √2) / (√3 + √2)(√3 - √2)

=> 1/√A = (√3 - √2) / [ (√3)² - (√2)² ]

=> 1/√A = (√3 - √2) / (3 - 2)

=> 1/√A = (√3 - √2) / 1

=> 1/√A = √3 - √2 -------(2)

Now,

Adding eq-(1) and (2) , we have ;

=> √A + 1/√A = √3 + √2 + √3 - √2

=> √A + 1/√A = 2√3

Hence,

The required value of √A + 1/√A is 2√3.