Given x + 1/x = 5, find x³ + 1/x³

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Accepted Answer

**Steps:**

1. Let $t=x+\frac{1}{x}=5$.
2. Then $x^2+\frac{1}{x^2}=t^2-2=25-2=23$.
3. Use identity $x^3+\frac{1}{x^3}=(x+\frac{1}{x})\bigl(x^2+\frac{1}{x^2}-1\bigr)=t(23-1)$.
4. So $x^3+\frac{1}{x^3}=5	imes22=110$.

FINAL_ANSWER: b

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Answer

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