1-2-a-b-a-b-min-

Question Number 145530 by mathdanisur last updated on 05/Jul/21

{(\frac{1}{2} + \frac{∣ a ∣ + ∣ b ∣}{∣ a + b ∣})}_{m i n} = ?

Answered by puissant last updated on 07/Jul/21

∣ a + b ∣⩽∣ a ∣ + ∣ b ∣ \Rightarrow \frac{∣ a ∣ + ∣ b ∣}{∣ a + b ∣} ⩾ 1

\Rightarrow (\frac{1}{2} + \frac{∣ a ∣ + ∣ b ∣}{∣ a + b ∣}) ⩾ \frac{3}{2}

take \min = \frac{3}{2} . .

Commented by mathdanisur last updated on 07/Jul/21

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