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Category: Algebra

find-the-radii-of-all-circles-with-center-C-tangenting-the-curve-h-C-5-1-h-x-2-y-2-1-

Question Number 123426 by MJS_new last updated on 25/Nov/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{radii}\:\mathrm{of}\:\mathrm{all}\:\mathrm{circles}\:\mathrm{with}\:\mathrm{center}\:{C} \\ $$$$\mathrm{tangenting}\:\mathrm{the}\:\mathrm{curve}\:{h} \\ $$$${C}=\begin{pmatrix}{\mathrm{5}}\\{\mathrm{1}}\end{pmatrix} \\ $$$${h}:\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{1} \\ $$ Commented by ajfour last updated…

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}}…