If m + 1/m = 8, what is the value of m^3 + 1/m^3?
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\(m+\frac{1}{m}=8\\ m^2-8m+1=0\\ \color{blue}m\in \{4-\sqrt{15},4+\sqrt{15}\}\)
If \(m\in \{4-\sqrt{15},4+\sqrt{15}\}\), then \(m^3+\dfrac{1}{m^3}=488\)
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