Question

If z^2+1/z^2=34 find the value of z^3+1/z^3

Answer 1

z² + 1/z² = 34
(z + 1/z)² -2 = 34
(z + 1/z)² = 36
(z + 1/z) = 6

now,
z³ + 1/z³ = (z + 1/z)³ -3(z + 1/z)
= (6)³ - 3(6)
= 216 - 18
= 198

Answer 2

Answer:

Step-by-step explanation:

(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