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Let \(a, b,\) and \(c\) be distinct real numbers such that \(\frac{a^3 + 6}{a} = \frac{b^3 + 6}{b} = \frac{c^3 + 6}{c}.\) Find \(a^3 + b^3 + c^3.\)

 Sep 23, 2022
 #1
avatar+33338 
+2

By inspection:

 

\(\frac{1^3+6}{1}=7\)

 

\(\frac{2^3+6}{2}=7\)

 

Unfortunately  \(\frac{3^3+6}{3}\ne7\) 

 

However \(\frac{(-3)^3+6}{-3}=7\)

 

I'll leave you to finish.

 Sep 23, 2022
 #2
avatar+95 
0

tysm!!! the answer is -18 for anyone wondering :)

WorldEndSymphony  Sep 24, 2022

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