Let-a-b-c-be-positive-real-numbers-with-sum-3-Prove-that-1-a-1-b-1-c-3-2a-2-bc-3-2b-2-ac-3-2c-2-ab-

Tinku Tara June 4, 2023 None 0 Comments

Question Number 149244 by EDWIN88 last updated on 04/Aug/21

Let a,b,c be positive real numbers with sum 3. Prove that (1/a)+(1/b)+(1/c) ≥ (3/(2a^2 +bc))+(3/(2b^2 +ac))+(3/(2c^2 +ab))

$$\:\:{Let}\:{a},{b},{c}\:{be}\:{positive}\:{real}\:{numbers} \\ $$$${with}\:{sum}\:\mathrm{3}.\:{Prove}\:{that}\: \\ $$$$\:\:\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{2}{a}^{\mathrm{2}} +{bc}}+\frac{\mathrm{3}}{\mathrm{2}{b}^{\mathrm{2}} +{ac}}+\frac{\mathrm{3}}{\mathrm{2}{c}^{\mathrm{2}} +{ab}} \\ $$

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Let-a-b-c-be-positive-real-numbers-with-sum-3-Prove-that-1-a-1-b-1-c-3-2a-2-bc-3-2b-2-ac-3-2c-2-ab-

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