Question

If x = 1/5-x and x≠5 find x3 + 1/x3

Answer 1

Answer:

$x = \frac{1}{5 - x} = \frac{1}{5} - \frac{1}{x} \\ x + \frac{1}{x} = \frac{1}{5} \\ {(x + \frac{1}{x})}^{3} = {x}^{3} + \frac{1}{ {x}^{3} } + 3(x + \frac{1}{x} ) \\ {(\frac{1}{5} )}^{3} = {x}^{3} + \frac{1}{ {x}^{3} } + 3( \frac{1}{5} ) \\ \frac{1}{125} - \frac{3}{5} = {x}^{3} + \frac{1}{ {x}^{3} } \\ \frac{ - 74}{125} = {x}^{3} + \frac{1}{ {x}^{3} }$

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