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# Algebra

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If m + 1/m = 8, what is the value of m^3 + 1/m^3?

Jan 12, 2022

#1
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If m + 1/m = 8, what is the value of m^3 + 1/m^3?

Hello Guest!

$$m+\frac{1}{m}=8\\ m^2-8m+1=0\\ \color{blue}m\in \{4-\sqrt{15},4+\sqrt{15}\}$$

If  $$m\in \{4-\sqrt{15},4+\sqrt{15}\}$$,  then  $$m^3+\dfrac{1}{m^3}=488$$

!

Jan 12, 2022