if-a-b-c-gt-0-and-1-a-b-1-b-c-1-c-a-4-then-1-a-1-b-1-c-9-a-b-c-16-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 156574 by MathSh last updated on 12/Oct/21

if a;b;c>0 and (1/(a+b)) + (1/(b+c)) + (1/(c+a)) = 4 then: (1/a) + (1/b) + (1/c) + (9/(a+b+c)) ≥ 16

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\frac{\mathrm{1}}{\mathrm{a}+\mathrm{b}}\:+\:\frac{\mathrm{1}}{\mathrm{b}+\mathrm{c}}\:+\:\frac{\mathrm{1}}{\mathrm{c}+\mathrm{a}}\:=\:\mathrm{4}\:\:\mathrm{then}: \\ $$$$\frac{\mathrm{1}}{\mathrm{a}}\:+\:\frac{\mathrm{1}}{\mathrm{b}}\:+\:\frac{\mathrm{1}}{\mathrm{c}}\:+\:\frac{\mathrm{9}}{\mathrm{a}+\mathrm{b}+\mathrm{c}}\:\geqslant\:\mathrm{16} \\ $$

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