Question

z square + 1 / z square = 18 , find z cube +- 1/ z cube

Answer 1

${z}^{2} + \frac{1}{ {z}^{2} } = 18 \\ {(z - \frac{1}{z}) }^{2} + 2 = 18 \\ z - \frac{1}{z} = \sqrt{16} = + 4 \: \: or \: \: - 4$

${z}^{3} - \frac{1}{ {z}^{3} } = {(z - \frac{1}{z}) }^{3} + 3(z - \frac{1}{z} ) \\ = {( + \: or \: - 4)}^{3} + 3 \times ( + \: or \: - 4) \\ = + \: or \: - 64 \: \: \: + \: \: \: or - 12 \\ = + \: or \: - 76$

Answer 2

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