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Category: Algebra

In-ABC-holds-2-3-tan-B-2-1-3-tan-2-A-2-9-2-

Question Number 188898 by Shrinava last updated on 08/Mar/23 $$\mathrm{In}\:\bigtriangleup\mathrm{ABC}\:\mathrm{holds}:\:\:\:\Sigma\:\frac{\mathrm{2}\:+\:\sqrt{\mathrm{3}}\:\mathrm{tan}\:\frac{\mathrm{B}}{\mathrm{2}}}{\mathrm{1}\:+\:\mathrm{3}\:\mathrm{tan}^{\mathrm{2}} \:\frac{\mathrm{A}}{\mathrm{2}}}\:\geqslant\:\frac{\mathrm{9}}{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-57818

Question Number 57818 by Tawa1 last updated on 12/Apr/19 Answered by tanmay.chaudhury50@gmail.com last updated on 13/Apr/19 $$\frac{{a}^{} +{b}+{c}}{\mathrm{3}}\geqslant\left({abc}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$$\frac{\mathrm{1}}{\mathrm{27}}\geqslant{abc}\:\:\:{let}\:{abc}=\frac{\mathrm{1}}{\mathrm{27}}−\delta \\ $$$${LHS} \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}\left(\frac{{a}^{\mathrm{2}} }{{b}}+\frac{{b}^{\mathrm{2}}…

If-a-b-c-1-a-2-b-2-c-2-2-a-3-b-3-c-3-3-then-a-5-b-5-c-5-

Question Number 57791 by Tawa1 last updated on 12/Apr/19 $$\:\mathrm{If}\:\:\:\:\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:\:=\:\:\mathrm{1}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{c}^{\mathrm{3}} \:\:=\:\:\mathrm{3}\:\: \\ $$$$\mathrm{then}\:\:\:\:\:\:\mathrm{a}^{\mathrm{5}} \:+\:\mathrm{b}^{\mathrm{5}} \:+\:\mathrm{c}^{\mathrm{5}\:\:} =\:\:?…