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Question Number 197325 by sonukgindia last updated on 13/Sep/23 Answered by witcher3 last updated on 13/Sep/23 $$\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{1} \\ $$$$\mathrm{if}\:\mathrm{x}\in\mathbb{R}\:\mid\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)=\mathrm{x}\Rightarrow\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{x}\in\left\{\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}},\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\right\} \\…

Question Number 197272 by Erico last updated on 12/Sep/23 $$\mathrm{How}\:\mathrm{to}\:\mathrm{calculate}\:\mathrm{this}\:\mathrm{integral} \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{ln}\left(\mathrm{1}+{sint}\right)}{{sint}}{dt} \\ $$ Answered by Mathspace last updated on 12/Sep/23 $${tan}\left(\frac{{t}}{\mathrm{2}}\right)={x}\:\Rightarrow \\…

Question Number 197299 by bbbbbbbb last updated on 12/Sep/23 $$\sqrt[{\mathrm{6}}]{−\mathrm{64}}−\sqrt[{\mathrm{10}}]{−\mathrm{10}}=? \\ $$$$\boldsymbol{{I}}\:\boldsymbol{\mathrm{need}}\:\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{much}}\:\boldsymbol{\mathrm{plz}} \\ $$ Answered by Frix last updated on 13/Sep/23 $$\forall{n}\in\mathbb{N}\backslash\left\{\mathrm{0}\right\}:\:−{n}={n}\mathrm{e}^{\mathrm{i}\pi} \:\Rightarrow \\ $$$$\sqrt[{{k}}]{−{n}}=\sqrt[{{k}}]{{n}}\mathrm{e}^{\mathrm{i}\frac{\pi}{{k}}}…

Question Number 197245 by sonukgindia last updated on 11/Sep/23 Commented by mr W last updated on 26/Sep/23 $${see}\:{Q}#\mathrm{197680} \\ $$ Terms of Service Privacy Policy…

Question Number 197253 by sciencestudentW last updated on 11/Sep/23 $$\mathrm{lo}\underset{\mathrm{3}} {\mathrm{g}12}={a} \\ $$$$\mathrm{log}\underset{\mathrm{3}} {\:}\mathrm{18}=?\: \\ $$ Answered by AST last updated on 11/Sep/23 $$\frac{{log}\mathrm{3}+\mathrm{2}{log}\mathrm{2}}{{log}\mathrm{3}}={a}\Rightarrow\mathrm{2}{log}\mathrm{2}=\left({a}−\mathrm{1}\right){log}\mathrm{3} \\…