Type = x+ 1/x 
Important Tricks and Concepts 

1) if x+1/x = a , then x² + 1/x² = a²-2 
2) if x-1/x = a , then x² + 1/x² = a²+2 
3) if x+1/x = a , then x³ + 1/x³ = a³-3a
4) if x-1/x = a , then x³ - 1/x³ = a³+3a  
5) if x+1/x = a , then x⁴ + 1/x⁴ = a⁴-4a²+2
6) if x-1/x = a , then x⁴ + 1/x⁴ = a⁴+4a²+2 
7) if x+1/x = a , then x⁵ + 1/x⁵ = a^5-5a³+5a
8) if x+1/x = a , then x⁶ + 1/x⁶ = a⁶-6a⁴+9a²-2