KöMaL 2021 B5204

Let $1\le a, b, c, d\le 4$ denote real numbers. Prove that $16\le (a+b+c+d)\left(\frac{1}a+\frac{1}b+\frac{1}c+\frac{1}d\right)\le 25.$

Official text KöMaL. Quoted with source.

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