If a = 2 + √3, find 1/a, (a – 1/a):

If a = 2 + √3, find 1/a, (a – 1/a)

Solution:

Given:

a = 2 + √3

So,

1/a = 1/ (2 + √3)

By rationalizing the denominator,

1/ (2 + √3) = [1(2 – √3)] / [(2 + √3) (2 – √3)]

= [(2 – √3)] / [2² – (√3)²]

= [(2 – √3)] / [4 – 3]

= (2 – √3)

Then,

a – 1/a = 2 + √3 – (2 – √3)

= 2 + √3 – 2 + √3

= 2√3

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