Question

LISTEN!!solve it plz​

Answer 1

$Question \: \: Number \: \: 08 \\ \\ x {}^{3} - \frac{1}{x {}^{3} } = 14 \: \: \: \: \: \: \: \: \: \: find \: \: \: x - \frac{1}{x} \\ \\ Answer \: \\ \\ let \: \: \: x - \frac{1}{x} = z \\ \\ cubing \: on \: both \: sides \: we \: have \\ \\ (x - \frac{1}{x} ) {}^{3} = z {}^{3} \\ \\ x {}^{3} - \frac{1}{x {}^{3} } - 3(x - \frac{1}{x} ) = z {}^{3} \\ \\ 14 - 3z = z {}^{3} \\ \\ z {}^{3} + 3z - 14 = 0 \\ \\ (z - 2)(z {}^{2} + 2z + 7) = 0 \\ \\ (z - 2) = 0 \: \: \: \: \: \: or \: \: \: \: \: \: z {}^{2} + 2z + 7 = 0 \\ \\ z = \frac{ - 2 + \sqrt{4 - 28} }{2} \: \: \: or \: \: \: z = \frac{ - 2 - \sqrt{4 - 28} }{2} \\ \\ z = \frac{ - 2 + \sqrt{ - 24} }{2} \: \: \: or \: \: \: z = \frac{ - 2 - \sqrt{ - 24} }{2} \\ \\ \\ therefore \: \: \: \: \: \\ \\ x - \frac{1}{x} = 2 \: \: \: \: or \: \: \: x - \frac{1}{x} = \frac{ - 2 + \sqrt{ - 24} }{2} \\ \\ or \\ \\ x - \frac{1}{x} = \frac{ - 2 - \sqrt{ - 24} }{2}$