Question

if (z²+1/z²) =18, find the value of z³-1/z³, using only the positive value of z-1/z..
Please answer fast it's urgent...............

Answer 1

(z²+1/z²)=18
(z-1/z)²=z²+1/z²-2
(z-1/z)²=18-2
(z-1/z)²=16
z-1/z=√16=4

(z-1/z)³=4³

z³-1/z³-3(z-1/z)=64
z³-1/z³-3×4=64
z³-1/z³=64+12
z³-1/z³=76

Answer 2

Given ,
          z² +1/z² = 18 
subtracting 2 ( z/z) from both sides
 => z² + 1/z² - 2 z * 1/z = 18 - 2
= > ( z-1/z )² = 16
Therefore , z - 1/z = 4
we know that  , 
a³ - b³ = (a - b ) ( a² + b² + ab )
=> z³ - 1/z³ = ( 4 )  ( 18 + z/z)
z³ - 1/z³ = 76