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Category: Arithmetic

simplify-t-26-3-3-5-1-3-26-3-3-5-1-3-

Question Number 155428 by ajfour last updated on 30/Sep/21 $${simplify} \\ $$$${t}=\left(\frac{\mathrm{26}}{\mathrm{3}\sqrt{\mathrm{3}}}+\mathrm{5}\right)^{\mathrm{1}/\mathrm{3}} −\left(\frac{\mathrm{26}}{\mathrm{3}\sqrt{\mathrm{3}}}−\mathrm{5}\right)^{\mathrm{1}/\mathrm{3}} \\ $$ Answered by peter frank last updated on 30/Sep/21 $$\mathrm{t}=\left(\frac{\mathrm{26}+\mathrm{15}\sqrt{\mathrm{3}}}{\mathrm{3}\sqrt{\mathrm{3}}}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} −\left(\frac{\mathrm{26}−\mathrm{15}\sqrt{\mathrm{3}}}{\mathrm{3}\sqrt{\mathrm{3}}}\right)^{\frac{\mathrm{1}}{\mathrm{3}}}…

Question-89852

Question Number 89852 by M±th+et£s last updated on 19/Apr/20 Answered by mr W last updated on 19/Apr/20 $${F}_{{n}} =\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\left(\varphi^{{n}} −\psi^{{n}} \right)\:{with} \\ $$$$\varphi=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}},\:\psi=\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}=\mathrm{1}−\varphi=−\frac{\mathrm{1}}{\varphi} \\ $$$${x}^{{n}}…

Question-89461

Question Number 89461 by student work last updated on 17/Apr/20 Answered by mahdi last updated on 17/Apr/20 $$\mathrm{A}=\mathrm{x}+\frac{\mathrm{y}}{\mathrm{x}+\frac{\mathrm{y}}{\mathrm{x}+\frac{\mathrm{y}}{…}}}\Rightarrow\mathrm{A}=\mathrm{x}+\frac{\mathrm{y}}{\mathrm{A}}\Rightarrow \\ $$$$\mathrm{A}^{\mathrm{2}} =\mathrm{Ax}+\mathrm{y}\Rightarrow\mathrm{A}^{\mathrm{2}} −\mathrm{xA}−\mathrm{y}=\mathrm{0} \\ $$$$\mathrm{A}=\frac{\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{4y}}}{\mathrm{2}}\:\mathrm{or}\:\frac{\mathrm{x}−\sqrt{\mathrm{x}^{\mathrm{2}}…

Question-89320

Question Number 89320 by peter frank last updated on 16/Apr/20 Commented by Rio Michael last updated on 16/Apr/20 $$\mathrm{it}\:\mathrm{means}\:\mathrm{the}\:\mathrm{planet}\:\mathrm{has}\:\mathrm{to}\:\mathrm{be}\:\mathrm{the}\:\mathrm{dorminate}\:\mathrm{gravitational} \\ $$$$\mathrm{body}\:\mathrm{on}\:\mathrm{its}\:\mathrm{orbit}\:\mathrm{round}\:\mathrm{the}\:\mathrm{sun},\:\mathrm{basically}\:\mathrm{it}\:\mathrm{has}\:\mathrm{to}\:\mathrm{send}\:\mathrm{out} \\ $$$$\mathrm{all}\:\mathrm{bodies}\:\mathrm{from}\:\mathrm{its}\:\mathrm{orbit}. \\ $$…