Question

If p=5-2√6 find p^2-1/p^2

Answer 1

P =5-2√6

p^2 = (5-2√6)^2

Using Identity (a-b)^2 = a^2+b^2 -2ab

(5-2√6)^2

=25+24-20√6

=49-20√6

p^2-1

=49-20√6-1

=48-20√6

p^2-1/p^2

=48-20√6/49-20√6

By rationalizing the denominator

=48-20√6(49+20√6) / 49-20√6(49+20√6)

=2352 - 960√6 -980√6 -2400/49^2 - 20√6^2

= -48-1940√6 /2401 - 2400

=-48-1940√6

Answer 2

I think the question must be to find p^2 + 1/p^2
If p = 5-2√6
then 1/p = 1/5-2√6
= 5+2√6 (When you rationalise the denominator)
p*1/p = 1
p+1/p = 5-2√6+(5+2√6)
       = 10
(p+1/p)^2 = 10^2
p^2 +1/p^2 +2(p*1/p) =100
p^2 +1/p^2 +2 = 100
p^2 +1/p^2 = 100-2
   = 98