Question Number 202638 by depressiveshrek last updated on 31/Dec/23 $$\sqrt{{x}−\frac{\mathrm{1}}{{x}}}−\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}=\mathrm{1}−\frac{\mathrm{1}}{{x}} \\ $$ Commented by AST last updated on 31/Dec/23 $${x}=\mathrm{1}.{Suppose}\:{x}\neq\mathrm{1},{let}\:{a}=\sqrt{{x}−\frac{\mathrm{1}}{{x}}};{b}=\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}} \\ $$$${a}−{b}=\mathrm{1}−\frac{\mathrm{1}}{{x}};\left({a}+{b}\right)^{\mathrm{2}} =\mathrm{1}+{x} \\ $$$${a}^{\mathrm{2}}…
Question Number 202698 by Bambamamoudou last updated on 31/Dec/23 $${determine}\:{le}\:{reste}\:{de}\:{la}\:{division}\:{eucludienne}\:{de}\:\mathrm{2023}^{\mathrm{2019}} {par}\:\mathrm{13} \\ $$ Answered by Rasheed.Sindhi last updated on 01/Jan/24 $$\because\:{gcd}\left(\mathrm{2023},\mathrm{13}\right)=\mathrm{1} \\ $$$$\therefore\:\:\:\:\mathrm{2023}^{\phi\left(\mathrm{13}\right)} \equiv\mathrm{1}\left({mod}\:\mathrm{13}\right) \\…
Question Number 202694 by Mingma last updated on 31/Dec/23 Answered by a.lgnaoui last updated on 01/Jan/24 $$\Delta\boldsymbol{\mathrm{KTP}} \\ $$$$ \\ $$ Commented by a.lgnaoui last…
Question Number 202589 by mnjuly1970 last updated on 30/Dec/23 $$ \\ $$$$\:\:\Omega\:=\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{k}}\:+\:\mathrm{2}{ln}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}{k}}\right)\right)=?\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$ Commented by mnjuly1970 last updated…
Question Number 202591 by Calculusboy last updated on 30/Dec/23 Answered by mr W last updated on 30/Dec/23 $$\frac{{dy}}{{dx}}+\mathrm{1}+\frac{{y}}{{x}}=\mathrm{0} \\ $$$${let}\:{y}={xt} \\ $$$$\frac{{dy}}{{dx}}={t}+{x}\frac{{dt}}{{dx}} \\ $$$${t}+{x}\frac{{dt}}{{dx}}+\mathrm{1}+{t}=\mathrm{0} \\…
Question Number 202616 by hardmath last updated on 30/Dec/23 $$\mathrm{If}\:\:\:\:\:\frac{\mathrm{a}}{\mathrm{a}\:+\:\mathrm{b}}\:−\:\frac{\mathrm{1}\:−\:\mathrm{a}}{\mathrm{a}\:−\:\mathrm{b}}\:=\:\mathrm{x} \\ $$$$\mathrm{Find}\:\:\:\:\:\frac{\mathrm{1}\:−\:\mathrm{b}}{\mathrm{a}\:−\:\mathrm{b}}\:+\:\frac{\mathrm{b}}{\mathrm{a}\:+\:\mathrm{b}}\:=\:? \\ $$ Answered by MATHEMATICSAM last updated on 30/Dec/23 $$\frac{{a}}{{a}\:+\:{b}}\:−\:\frac{\mathrm{1}\:−\:{a}}{{a}\:−\:{b}}\:=\:{x} \\ $$$$\Rightarrow\:\frac{{a}}{{a}\:+\:{b}}\:−\:\mathrm{1}\:−\:\frac{\mathrm{1}\:−\:{a}}{{a}\:−\:\:{b}}\:−\:\mathrm{1}\:=\:{x}\:−\:\mathrm{2} \\…
Question Number 202584 by cortano12 last updated on 30/Dec/23 $$\:\:\: \\ $$ Answered by dimentri last updated on 30/Dec/23 $$\mathrm{2}\:\begin{pmatrix}{\mathrm{m}}\\{\mathrm{2}}\end{pmatrix}\:−\:\mathrm{4m}\:=\:\mathrm{84} \\ $$$$\:\mathrm{m}^{\mathrm{2}} −\mathrm{5m}−\mathrm{84}\:=\:\mathrm{0} \\ $$$$\:\mathrm{m}\:=\:\mathrm{12}\:…
Question Number 202581 by Frix last updated on 30/Dec/23 Commented by Frix last updated on 30/Dec/23 $$\mathrm{An}\:\mathrm{easy}\:\mathrm{one}:\:\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle}. \\ $$ Answered by mr W last updated…
Question Number 202614 by a.lgnaoui last updated on 30/Dec/23 $$\mathrm{find}\:\mathrm{x} \\ $$$$ \\ $$ Commented by a.lgnaoui last updated on 30/Dec/23 Commented by a.lgnaoui last…
Question Number 202636 by ibroclex_adex last updated on 30/Dec/23 $$\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\:^{\mathrm{3}} \sqrt{\mathrm{4}^{\mathrm{5}−\mathrm{x}} }}{\int_{\mathrm{4}} ^{\mathrm{6}} \left(\mathrm{x}−\mathrm{1}\right){dx}}\:=\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2x}−\mathrm{1}} }\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline{\mathrm{Solution}}…