Question

$if \: (x + 1 \div x) = x \\ then \: find(x {}^{3} + 1 \div x {}^{3} )$
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Answer 1

$Answer \: \\ \\ Given \: \: \: \: x + \frac{1}{x} = x \: \: \: \: \: find \: \: x {}^{3} + \frac{1}{x {}^{3} } \\ \\ x + \frac{1}{x} = x \\ \\ Cubing \: \: on \: both \: sides \: we \: have \\ \\ (x + \frac{1}{x} ) {}^{3} = x {}^{2} \\ \\ x {}^{3} + \frac{1}{x {}^{3} } + 3(x + \frac{1}{x} ) = x {}^{3} \\ \\ x {}^{3} + \frac{1}{x {}^{3} } + 3x = x {}^{3} \\ \\ x {}^{3} + \frac{1}{x {}^{3} } = x {}^{3} - 3x \\ \\ therefore \: \: \: x {}^{3} + \frac{1}{x {}^{ 3} } = x {}^{3} - 3x \\ \\ NOTE \: \\ \\ ( \alpha + \frac{1}{ \beta } ) {}^{3} = \alpha {}^{3} + \frac{1}{ \beta {}^{3} } + 3 \alpha \beta ( \alpha + \frac{1}{ \beta } )$

Answer 2

Step-by-step explanation:

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