An algebra problem by Aryan Gupta

Algebra Level 3

If a2+b2+c2+1a2+1b2+1c2=6,a^2 + b^2 + c^2 +\frac1{a^2}+ \frac{1}{b^2} + \frac1{c^2} = 6, find the smallest possible value of a3+b3+c3.a^3 + b^3 + c^3.

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