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if-13-1-and-1-find-the-quadratic-equation-whose-roots-are-3-4-4-3-1-and-2-5-6-6-5-6-

Question Number 90947 by Cynosure last updated on 27/Apr/20 $${if}\:\alpha^{\mathrm{13}} =\mathrm{1}\:{and}\:\alpha\neq\mathrm{1},{find}\:{the}\:{quadratic}\:\:{equation} \\ $$$${whose}\:{roots}\:{are}\:\left(\alpha+\alpha^{\mathrm{3}} +\alpha^{\mathrm{4}} +\alpha^{−\mathrm{4}} +\alpha^{−\mathrm{3}} +\alpha^{−\mathrm{1}} \right)\:{and}\:\left(\alpha^{\mathrm{2}} +\alpha^{\mathrm{5}} +\alpha^{\mathrm{6}} +\alpha^{−\mathrm{6}} +\alpha^{−\mathrm{5}} +\alpha^{−\mathrm{6}} \right) \\…

f-x-x-1-3-is-there-an-inflection-point-when-x-0-

Question Number 90940 by  M±th+et+s last updated on 27/Apr/20 $${f}\left({x}\right)=\sqrt[{\mathrm{3}}]{{x}}\:\:{is}\:{there}\:{an}\:{inflection}\:{point} \\ $$$${when}\:{x}=\mathrm{0} \\ $$ Answered by MJS last updated on 27/Apr/20 $$\mathrm{if}\:\mathrm{we}\:\mathrm{stay}\:\mathrm{in}\:\mathbb{R}\:\Rightarrow\:\sqrt[{\mathrm{3}}]{−{x}}=−\sqrt[{\mathrm{3}}]{{x}} \\ $$$${f}\left({x}\right)=\sqrt[{\mathrm{3}}]{{x}}={x}^{\mathrm{1}/\mathrm{3}} \\…

Show-that-i-sin-1-2-2-2-in-air-if-the-refractive-index-n-sin-2-60-sin-2-45-

Question Number 156270 by Tawa11 last updated on 09/Oct/21 $$\mathrm{Show}\:\mathrm{that}\:\:\:\:\:\:\mathrm{i}\:\:\:\:=\:\:\:\mathrm{sin}^{−\:\mathrm{1}} \left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right)^{\mathrm{2}} \:\:\:\:\mathrm{in}\:\mathrm{air},\:\mathrm{if}\:\mathrm{the}\:\mathrm{refractive} \\ $$$$\mathrm{index}\:\:\:\:\:\:\:\:\mathrm{n}\:\:\:=\:\:\:\frac{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{60}\right)}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{45}\right)} \\ $$ Commented by Tawa11 last updated on 10/Oct/21…

and-are-the-roots-of-x-3-9x-9-0-find-the-value-of-1-3-3-3-2-5-5-5-

Question Number 90709 by Cynosure last updated on 25/Apr/20 $$\alpha,\beta\:{and}\:\gamma\:{are}\:{the}\:{roots}\:{of}\:\:{x}^{\mathrm{3}} −\mathrm{9}{x}+\mathrm{9}=\mathrm{0} \\ $$$${find}\:{the}\:{value}\:{of}\:\left(\mathrm{1}\right)\:\alpha^{−\mathrm{3}} +\beta^{−\mathrm{3}} +\gamma^{−\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{2}\right)\:\alpha^{−\mathrm{5}} +\beta^{−\mathrm{5}} +\gamma^{−\mathrm{5}} \\ $$ Commented by jagoll last…

Question-90647

Question Number 90647 by I want to learn more last updated on 25/Apr/20 Commented by I want to learn more last updated on 25/Apr/20 $$\mathrm{For}\:\mathrm{the}\:\mathrm{string}\:\mathrm{to}\:\mathrm{be}\:\mathrm{kept}\:\mathrm{tight},\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{relationship}\:\mathrm{between}…