If a - 1/a = 2 then show that

Question

( a + 1/a )^2 = 8

Answer 1

from the given:
a -1/a = 2
let's square both sides
(a - 1/a)^2 = 4
a^2 - 2 + 1/a^2 = 4
a^2 + 1/a^2 = 6

starting with
(a + 1/a)^2
= a^2 + 2 + 1/a^2
= a^2 + 1/a^2 + 2
= 6+2
= 8