No Ordinary Optimization Problem

Calculus Level 3

If a,b,c>0a, b, c>0 and a+b+c=1a+b+c=1, the minimum value of (a+1a)10+(b+1b)10+(c+1c)10(a+\frac{1}{a})^{10}+(b+\frac{1}{b})^{10}+(c+\frac{1}{c})^{10} can be expressed as 10d3e\frac{10^{d}}{3^{e}} where dd and ee are positive integers. Find d+ed+e

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