Question

If x plus 1 by x is equal to 4, find the value of x cube plus 1 by x cube. ​

Answer 1

Answer:

$x + \frac{1}{x} = 4 \\( cubing \: both \: sides) \\ {(x + \frac{1}{x} )}^{3} = 64 \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) = 64 \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times 4 = 64 \\ {x}^{3} + \frac{1}{ {x}^{3} } = 52$

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