Question

if x2+1/X=10/3 find x3-1/x3​

Answer 1

Answer:

There is a mistake in question it should be X²+1/X².

Answer 2

Answer:

$\frac{ {x}^{2} + 1}{x} = \frac{10}{3} \\ 3 {x}^{2} + 3 = 10x \\ 3 {x}^{2} - 10x + 3 = 0 \\( x - 9)(x - 1) = 0 \\ x = 9 \: (or) \: x = 1$

$finding \: \frac{ {x}^{3} - 1 }{ {x}^{3} } \\ \\ if \: x = 1 ...then\\ \frac{ {x}^{3} - 1 }{ {x}^{3} } = \frac{ {x}^{3} }{ {x}^{3} } - \frac{1}{ {x}^{3} } \\ = 1 - \frac{1}{ {1}^{3} } \\ = 1 - 1 \\ = 0 \\ if \: x = 9...then \\ = \frac{729}{729} - \frac{1}{729} \\ = 1 - \frac{1}{729} \\ = \frac{729 - 1}{729} \\ = \frac{728}{729} \\ = 0.999$

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