Prove-that-2a-a-b-2b-b-c-2c-c-a-3-where-a-b-c-be-positive-real-numbers-

Question Number 7022 by Master Moon last updated on 06/Aug/16

$$\mathrm{Prove}\:\mathrm{that}\:\sqrt{\frac{\mathrm{2a}}{\mathrm{a}+\mathrm{b}}}\:+\:\sqrt{\frac{\mathrm{2b}}{\mathrm{b}+\mathrm{c}}}\:+\:\sqrt{\frac{\mathrm{2c}}{\mathrm{c}+\mathrm{a}}}\:\leqslant\:\mathrm{3} \\ $$$$\:{where}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers} \\ $$

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