Let-a-b-c-be-positive-real-numbers-such-that-a-b-c-1-Prove-that-ab-1-c-2-bc-1-a-2-ca-1-b-2-3-8-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 150040 by bobhans last updated on 09/Aug/21

Let a,b,c be positive real numbers such that a+b+c=1 .Prove that ((ab)/(1−c^2 )) +((bc)/(1−a^2 ))+((ca)/(1−b^2 )) ≤ (3/8)

$$\mathrm{Let}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{1}\:.\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\:\frac{\mathrm{ab}}{\mathrm{1}−\mathrm{c}^{\mathrm{2}} }\:+\frac{\mathrm{bc}}{\mathrm{1}−\mathrm{a}^{\mathrm{2}} }+\frac{\mathrm{ca}}{\mathrm{1}−\mathrm{b}^{\mathrm{2}} }\:\leqslant\:\frac{\mathrm{3}}{\mathrm{8}} \\ $$

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Let-a-b-c-be-positive-real-numbers-such-that-a-b-c-1-Prove-that-ab-1-c-2-bc-1-a-2-ca-1-b-2-3-8-

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