If x-1 - x-3- find x2-1 - x2 and x3-1 - x3

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Cube Root Using Prime Factorisation

If x+1 / x=3,...

Question

If x + (1/x) = 3, find x² + (1/x²) and x³ + (1/x³)

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If $x + \frac{1}{x} = 3$ , calculate $x^{2} + \frac{1}{x^{2}}, x^{3} + \frac{1}{x^{3}} a n d x^{4} + \frac{1}{x^{4}}$ .

\frac{x^{2} + 1}{x} = 3 \frac{1}{3}

x^{3} - \frac{1}{x^{3}}

\frac{x^{2} + 1}{x} = 3 \frac{1}{3}

x > 1

x^{3} - \frac{1}{x^{3}}

x = 9 - 4 \sqrt{5}

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