TR-MO-R1 2018 Problem 31

$0 < x \le 1$ olmak üzere, $\sqrt{1+\dfrac{4}{x}} - \sqrt{1-x}$ ifadesinin alabileceği en küçük değer nedir?

a) $1$ b) $2$ c) $3-\dfrac{1}{\sqrt{2}}$ d) $\sqrt{5}$ e) Hiçbiri

Official text Turkish Mathematical Olympiad, first round 2018 official paper, page 10. Quoted with source.

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