Question Number 206108 by MATHEMATICSAM last updated on 07/Apr/24 $$\mathrm{If}\:{x}\:=\:\sqrt{\frac{\sqrt{\mathrm{5}}\:+\:\mathrm{1}}{\:\sqrt{\mathrm{5}}\:−\:\mathrm{1}}}\:\mathrm{then}\:{x}^{\mathrm{12}} \:=\:? \\ $$ Answered by mr W last updated on 07/Apr/24 $${x}=\sqrt{\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\:\sqrt{\mathrm{5}}−\mathrm{1}}}=\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{2}}=\varphi \\ $$$${x}^{\mathrm{2}} ={x}+\mathrm{1}…
Question Number 206104 by cortano21 last updated on 07/Apr/24 $$\:\:\:\:\downharpoonleft\underline{\:} \\ $$ Answered by dimentri last updated on 07/Apr/24 $$\:\:\mathrm{7}^{−\mathrm{a}} =\:\mathrm{3}^{−\mathrm{b}} =\:\mathrm{2}^{−\mathrm{c}} =\mathrm{5}^{−\mathrm{d}} =\:\mathrm{m} \\…
Question Number 206129 by hardmath last updated on 07/Apr/24 Answered by MaruMaru last updated on 07/Apr/24 $${constant}\:\mathcal{C}\:??? \\ $$$${is}\:{it}\:{potter}\:{const}??? \\ $$$$ \\ $$https://ko.m.wikipedia.org/wiki/%ED%8F%AC%ED%84%B0_%EC%83%81%EC%88%98 Commented by…
Question Number 206074 by MATHEMATICSAM last updated on 06/Apr/24 $$\left({x}_{\mathrm{1}} \:−\:{x}_{\mathrm{2}} \:+\:{x}_{\mathrm{3}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{2}} \left({x}_{\mathrm{4}} \:+\:{x}_{\mathrm{5}} \:−\:{x}_{\mathrm{2}} \right) \\ $$$$\left({x}_{\mathrm{2}} \:−\:{x}_{\mathrm{3}} \:+\:{x}_{\mathrm{4}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{3}} \left({x}_{\mathrm{5}}…
Question Number 206066 by hardmath last updated on 06/Apr/24 $$\mathrm{Find}: \\ $$$$\frac{\mathrm{3}}{\mathrm{4}}\:\centerdot\:\frac{\mathrm{8}}{\mathrm{9}}\:\centerdot\:\frac{\mathrm{15}}{\mathrm{16}}\:\centerdot\:…\:\centerdot\:\frac{\mathrm{120}}{\mathrm{121}}\:=\:? \\ $$ Answered by mr W last updated on 06/Apr/24 $$\underset{{n}=\mathrm{2}} {\overset{\mathrm{11}} {\prod}}\frac{{n}^{\mathrm{2}}…
Question Number 206063 by MATHEMATICSAM last updated on 06/Apr/24 $$\mathrm{If}\:\left({x}\:+\:\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\right)\left({y}\:+\:\sqrt{\mathrm{1}\:+\:{y}^{\mathrm{2}} }\right)\:=\:\mathrm{1}\:\mathrm{then} \\ $$$$\mathrm{find}\:\left({x}\:+\:{y}\right)^{\mathrm{2}} . \\ $$ Answered by mr W last updated on 06/Apr/24…
Question Number 206082 by hardmath last updated on 06/Apr/24 $$\mathrm{If}\:\:\:\mathrm{cos}\boldsymbol{\alpha}\:=\:\mathrm{sin}\boldsymbol{\alpha}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$$$\mathrm{Find}\:\:\:\mathrm{sin2}\boldsymbol{\alpha}\:=\:? \\ $$ Answered by MATHEMATICSAM last updated on 29/Apr/24 $$\mathrm{cos}\alpha\:=\:\mathrm{sin}\alpha\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$$$\Rightarrow\:\mathrm{cos}\alpha\:−\:\mathrm{sin}\alpha\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\…
Question Number 206025 by cortano12 last updated on 05/Apr/24 $$\:\:\:\:\:\mathrm{2}^{\mathrm{2024}} \:=\:{x}\:\left({mod}\:\mathrm{10}\right)\: \\ $$ Answered by BaliramKumar last updated on 05/Apr/24 $$\mathrm{Find}\:\mathrm{unit}\:\mathrm{digit} \\ $$$$\mathrm{2}^{\mathrm{2024}} \:=\:\mathrm{2}^{\mathrm{4k}\:+\:\mathrm{4}} \:=\:\mathrm{2}^{\mathrm{4}}…
Question Number 205988 by cortano12 last updated on 04/Apr/24 $$\:\:{Given}\:{f}\left({x}+\mathrm{1}\right)=\mathrm{2}^{{f}\left({x}\right)} .{f}\left(\mathrm{1}\right) \\ $$$$\:\:{and}\:{f}\left(\mathrm{1}\right)=\:\mathrm{16}\: \\ $$$$\:\:{then}\:{f}\left(\mathrm{2016}\right)=? \\ $$ Answered by Berbere last updated on 04/Apr/24 $${f}\left(\mathrm{2}\right)=\mathrm{2}^{\mathrm{20}}…
Question Number 205990 by MATHEMATICSAM last updated on 04/Apr/24 $$\mathrm{If}\:{x}\:=\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{then}\:\frac{\sqrt{\mathrm{1}\:+\:{x}}\:+\:\sqrt{\mathrm{1}\:−\:{x}}}{\:\sqrt{\mathrm{1}\:+\:{x}}\:−\:\sqrt{\mathrm{1}\:−\:{x}}}\:=\:? \\ $$ Answered by cortano12 last updated on 04/Apr/24 $$\:\frac{\left(\sqrt{\mathrm{1}+{x}}\:+\sqrt{\mathrm{1}−{x}}\:\right)^{\mathrm{2}} }{\mathrm{2}{x}}\:=\:\frac{\mathrm{2}+\mathrm{2}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{\mathrm{2}{x}}\: \\ $$$$\:=\:\frac{\mathrm{1}}{{x}}\:+\:\sqrt{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }−\mathrm{1}}\:…