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Given-that-and-are-the-roots-oc-the-equation-ax-2-bx-c-0-Show-that-b-2-ac-2-where-

Question Number 63154 by Rio Michael last updated on 29/Jun/19 $${Given}\:{that}\:\alpha\:{and}\:\beta\:{are}\:{the}\:{roots}\:{oc}\:{the}\:{equation}\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$$.\:{Show}\:{that}\:\:\:\lambda\mu{b}^{\mathrm{2}} =\:{ac}\left(\lambda\:+\:\mu\right)^{\mathrm{2}} ,\:{where}\:\frac{\alpha}{\beta}=\:\frac{\lambda}{\mu}. \\ $$ Commented by Prithwish sen last updated on…

tg-x-2-1-ctg-x-2-2sin-x-2-x-180-540-

Question Number 62982 by ANTARES VY last updated on 27/Jun/19 $$\frac{\boldsymbol{\mathrm{tg}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)−\mathrm{1}}{\boldsymbol{\mathrm{ctg}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)}=\mathrm{2}\boldsymbol{\mathrm{sin}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)\:\:\boldsymbol{\mathrm{x}}\in\left(\mathrm{180}°;\mathrm{540}°\right) \\ $$$$ \\ $$ Answered by MJS last updated on 27/Jun/19 $$\frac{\mathrm{1}}{\mathrm{cot}}=\mathrm{tan} \\ $$$$\mathrm{tan}^{\mathrm{2}}…

Question-128518

Question Number 128518 by shaker last updated on 08/Jan/21 Commented by bramlexs22 last updated on 08/Jan/21 $$\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{n}}} \:=\:\mathrm{u}\:\Rightarrow\:\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{n}}} \:+\:\mathrm{3}^{−\frac{\mathrm{1}}{\mathrm{n}}} \:=\:\frac{\mathrm{u}^{\mathrm{2}} +\mathrm{1}}{\mathrm{u}} \\ $$$$\mathrm{x}\:=\:\frac{\mathrm{u}^{\mathrm{2}} +\mathrm{1}}{\mathrm{2u}}\:\Rightarrow\:\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:=\:\frac{\mathrm{u}^{\mathrm{2}}…