Minimum Fraction Product

Algebra Level 3

Given positive reals a,b,c,da, b, c, d and ee, what is the minimum possible value of (a+b+c+d+e)(1a+4b+9c+16d+25e)?\small (a + b + c + d + e) \left( \frac {1}{a} + \frac {4}{b} + \frac {9} {c} + \frac {16}{d} + \frac {25}{e} \right)?

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