Question

If a=2+√3,Find the Value of

\sqrt{a}-\frac{1}{\sqrt{a}}and\ \ a-\frac{1}{a}
a
​
−
a
​

1
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and a−
a
1
​

Answer 1

Given:

a=2+√3

To find:

Find the Value of  \sqrt{a}-\frac{1}{\sqrt{a}}and\ \ a-\frac{1}{a}

⇒ Find the value of √a - 1/√a and a - 1/a

Solution:

From given, we have

a = 2 + √3

The value of √a - 1/√a

= √[2 + √3] - 1/√[2 + √3]

= [2 + √3 - 1]/√[2 + √3]

= [√3 + 1]/√[2 + √3]

The value of a - 1/a

= [2 + √3] - 1/[2 + √3]

= [(2 + √3)² - 1]/[2 + √3]

= [4 + 3 + 4√3 - 1]/√[2 + √3]

= [6 + 4√3]/√[2 + √3]

Therefore, the value of √a - 1/√a is [√3 + 1]/√[2 + √3] and the value of a - 1/a is [6 + 4√3]/√[2 + √3]