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

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

Answered by puissant last updated on 07/Jul/21

$$\mid \mathrm{a}+\mathrm{b}\mid ⩽\mid \mathrm{a}\mid +\mid \mathrm{b}\mid \Rightarrow \frac{\mid \mathrm{a}\mid +\mid \mathrm{b}\mid }{\mid \mathrm{a}+\mathrm{b}\mid }⩾1$$$$\Rightarrow (\frac{1}{2}+\frac{\mid \mathrm{a}\mid +\mid \mathrm{b}\mid }{\mid \mathrm{a}+\mathrm{b}\mid })⩾\frac{3}{2}$$$$\mathrm{take}\min =\frac{3}{2}..$$

Commented by mathdanisur last updated on 07/Jul/21

$$ThanksSer$$

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