Question

if z square+1/z square=11, find the value of z cube -1/z cube using only the positive values of z-1/z​

Answer 1

Answer:

$z {}^{2} + \: \frac{1}{z {}^{2} } = 11 \\ (z - \frac{1}{z} ) {}^{2} = (z {}^{2} + \frac{1}{z {}^{2} } ) - 2 = 11 - 2 = 9 \\ (z - \frac{1}{z}) = \sqrt{9} = 3 \\ (z - \frac{1}{z} ) {}^{3} = z {}^{3} - \frac{1}{z {}^{3} } + 3(z - \frac{1}{z} ) \\ 3 {}^{3} = z {}^{3} - \frac{1}{z {}^{3} } + 3 \times 3 \\ z {}^{3} - \frac{1}{z {}^{3} } = 3 {}^{3} - 3 \times 3 = 27 - 9 = 18 \\ thus \: \: \: \: z {}^{3} - \frac{1}{z {}^{3} } = 18$

Answer 2

Answer:

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