Question

If a= 5+2√6, then a- 1/a is equal to: (A) 4√6 (B) -4√6 (C) 10
(D) -10

Answer 1

Solution:

Option A is correct.

If a= 5+ 2√6

1/a=1/5+2√6

1/a = 1×( 5-2√6) / (5+2√6 )× (5-2√6)

By rationalising the denominator

1/a = 5-2√6 / (5² )- (2√6)²

[ (a+b)(a-b) = a²- b²]

1/a= 5-2√6 / 25 - 4×6

1/a= 5-2√6 / 25 - 24

1/a= 5-2√6 / 1 = 5-2√6

1/a = 5-2√6

a-1/a = 5+2√6 -(5-2√6)

a-1/a = 5+2√6 - 5 +2√6

a- 1/a = 2√6+2√6= 4√6

a- 1/a = 4√6

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Hope this will help you.......

Answer 2

Hey there!

a=5+2√6

1/a=1/5+2√6 * 5-2√6/ 5-2√6

= 5-2√6/5²-(2√6)²

=5-2√6/25-24=5-2√6.

a-1/a

=5+2√6-(5-2√6)

=5+2√6-5+2√6

=4√6

Option A is correct.