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If $x + \dfrac{1}{x} = 5$, find $x^3 + \dfrac{1}{x^3}$.

A$110$
B$125$
C$105$
D$100$
Answer & Solution
Correct answer: A. $110$
Using $(x+1/x)^3=x^3+1/x^3+3(x+1/x)$, we obtain $125=x^3+1/x^3+15$. Hence $x^3+1/x^3=110$, so option A is correct. Option B, $125$, results from omitting the cross-term $15$.
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