If a = 2 + √3 , then find the value of a - 1/a

Solution:

Given, a = 2 + √3

We have to find the value of a - 1/a.

1/a = 1/(2 + √3)

By rationalising,

1/(2 + √3) = 1/(2 + √3) × (2 - √3)/(2 - √3)

= (2 - √3) / (2 + √3)(2 - √3)

By using algebraic identity,

(a - b)² = a² - 2ab + b²

(2 + √3)(2 - √3) = (2)² - (√3)²

= 4 - 3

= 1

So, (2 - √3) / (2 + √3)(2 - √3) = (2 - √3) / (1)

= (2 - √3)

1/a = (2 - √3)

Now, a - 1/a = (2 + √3) - (2 - √3)

= 2 + √3 - 2 + √3

= 2√3

Therefore, the value of a - 1/a is 2√3.

✦ Try This: Find the values of a² - 1/a² if a = 1/(3 - 4√3).

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1

NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 12

If a = 2 + √3 , then find the value of a - 1/a

Summary:

Rationalization can be considered as the process used to eliminate a radical or an imaginary number from the denominator of an algebraic fraction. If a = 2 + √3 , then the value of a - 1/a is 2√3

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