If-a-b-c-are-the-sides-of-a-triangle-prove-the-following-inequality-a-c-a-b-b-a-b-c-c-b-c-a-3-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 24908 by Tinkutara last updated on 28/Nov/17

If a, b, c are the sides of a triangle prove the following inequality: (a/(c + a − b)) + (b/(a + b − c)) + (c/(b + c − a)) ≥ 3.

$$\mathrm{If}\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{prove} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{inequality}: \\ $$$$\frac{{a}}{{c}\:+\:{a}\:−\:{b}}\:+\:\frac{{b}}{{a}\:+\:{b}\:−\:{c}}\:+\:\frac{{c}}{{b}\:+\:{c}\:−\:{a}}\:\geqslant\:\mathrm{3}. \\ $$

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