Cauchy-Schwarz is pretty helpful

Algebra Level 2

Let aa, bb, cc and dd be positive reals such that a+b+c+d=1a + b + c + d = 1. Find the minimum value of 1a+1b+1c+1d\frac {1}{a} + \frac {1}{b} + \frac {1}{c} + \frac {1}{d}.

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