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Question Number 156867 by cortano last updated on 16/Oct/21

Answered by qaz last updated on 16/Oct/21

$$\frac{1}{\mathrm{a}+\mathrm{b}}+\frac{9}{\mathrm{c}}+\frac{16}{\mathrm{a}+\mathrm{b}+\mathrm{c}}⩾\frac{{(1+3+4)}^2}{2(\mathrm{a}+\mathrm{b}+\mathrm{c})}=8$$$$\mathrm{Min}=8\mathrm{holds}\mathrm{only}\mathrm{when}\frac{1}{\mathrm{a}+\mathrm{b}}=\frac{3}{\mathrm{c}}=\frac{4}{\mathrm{a}+\mathrm{b}+\mathrm{c}}\mathrm{ie}.\mathrm{a}+\mathrm{b}=1\mathrm{c}=3$$

Commented by cortano last updated on 16/Oct/21

$$Tittuslemma$$

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