Question Number 221017 by Rojarani last updated on 22/May/25
Answered by Ghisom last updated on 23/May/25
$$\mathrm{min}\:\left(\frac{{a}^{\mathrm{2}} }{{b}}+\frac{{b}^{\mathrm{2}} }{{c}}+\frac{{c}^{\mathrm{2}} }{{a}}\right)\:=\mathrm{1}\:\mathrm{when}\:{a}={b}={c}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\mathrm{min}\:\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} \right)\:=\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{when}\:{a}={b}={c}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\mathrm{1}\geqslant\frac{{k}}{\mathrm{3}}\:\Rightarrow\:\mathrm{max}\:\left({k}\right)\:=\mathrm{3} \\ $$