In-ABC-the-following-relationship-holds-a-3-b-3-c-3-h-a-3-h-b-3-h-c-3-5832-3-r-6-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 173426 by Shrinava last updated on 11/Jul/22

In △ABC the following relationship holds: (a^3 +b^3 +c^3 )(h_a ^3 +h_b ^3 +h_c ^3 ) ≥ 5832 (√3) r^6

$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{relationship} \\ $$$$\mathrm{holds}: \\ $$$$\left(\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} +\mathrm{c}^{\mathrm{3}} \right)\left(\mathrm{h}_{\boldsymbol{\mathrm{a}}} ^{\mathrm{3}} +\mathrm{h}_{\boldsymbol{\mathrm{b}}} ^{\mathrm{3}} +\mathrm{h}_{\boldsymbol{\mathrm{c}}} ^{\mathrm{3}} \right)\:\geqslant\:\mathrm{5832}\:\sqrt{\mathrm{3}}\:\mathrm{r}^{\mathrm{6}} \\ $$

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In-ABC-the-following-relationship-holds-a-3-b-3-c-3-h-a-3-h-b-3-h-c-3-5832-3-r-6-

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