Question Number 149588 by mathdanisur last updated on 06/Aug/21 $$\begin{cases}{{x}\:+\:\frac{\mathrm{1}}{{y}}\:=\:\mathrm{2}}\\{{y}\:+\:\frac{\mathrm{1}}{{z}}\:=\:\mathrm{2}}\\{{z}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{2}}\end{cases}\:\:\:\Rightarrow\:\:{x};{y};{z}=? \\ $$ Commented by Ar Brandon last updated on 06/Aug/21 $$\mathrm{1};\mathrm{1};\mathrm{1} \\ $$ Commented by…
Question Number 84047 by jagoll last updated on 09/Mar/20 $$\mathrm{how}\:\mathrm{many}\: \\ $$$$\mathrm{natural}\:\mathrm{solution}\:\mathrm{are}\:\mathrm{there}\:\mathrm{for}\: \\ $$$${x}^{\mathrm{2}} \:−\:{y}\:!\:=\:\mathrm{2019}\:. \\ $$ Answered by naka3546 last updated on 09/Mar/20 $$\mathrm{1},\:{sir}\:\:{namely}\:\:\left({x},\:{y}\right)\:=\:\left(\mathrm{45},\:\mathrm{3}\right)…
Question Number 149569 by mathdanisur last updated on 06/Aug/21 $$\underset{\boldsymbol{\mathrm{x}}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{5x}\:+\:\mathrm{6}}{\mathrm{2x}\:-\:\mathrm{9}}\right)^{\boldsymbol{\mathrm{x}}^{\mathrm{2}} } =\:? \\ $$ Answered by Ar Brandon last updated on 06/Aug/21 $$\mathscr{L}=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{5}{x}+\mathrm{6}}{\mathrm{2}{x}−\mathrm{9}}\right)^{{x}^{\mathrm{2}}…
Question Number 149568 by mathdanisur last updated on 06/Aug/21 $${solve}\:{the}\:{equation}: \\ $$$$\mathrm{20}{z}\left[{z}\right]\:-\:\mathrm{21}\left\{{z}\right\}\:=\:\mathrm{2021} \\ $$$${where}\:\left\{\ast\right\}\:{is}\:{GIF}\:\:{and}\:\:\left\{{z}\right\}\:=\:{z}\:-\:\left[{z}\right] \\ $$ Answered by Olaf_Thorendsen last updated on 06/Aug/21 $$\mathrm{20}{z}\left[{z}\right]−\mathrm{21}\left\{{z}\right\}\:=\:\mathrm{2021}\:\:\:\:\left(\mathrm{1}\right) \\…
Question Number 149567 by mathdanisur last updated on 06/Aug/21 $${if}\:\:\boldsymbol{{q}}\:\:{is}\:{prime}\:{number}\:{fixed},\:{then} \\ $$$${solve}\:{for}\:{natural}\:{numbers}\:{the}\:{equation}: \\ $$$$\frac{\mathrm{1}}{{q}}\:=\:\frac{\mathrm{1}}{{x}}\:+\:\frac{\mathrm{1}}{{y}}\:-\:\frac{\mathrm{1}}{{z}} \\ $$ Commented by Rasheed.Sindhi last updated on 07/Aug/21 $$\mathrm{My}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{too}\:\mathrm{lengthy}. \\…
Question Number 84014 by redmiiuser last updated on 08/Mar/20 $${find}\:{the}\:{no}.\:{of}\:{positivve} \\ $$$${integral}\:{solutions}\:{of} \\ $$$${x}+{y}+\mathrm{2}{z}=\mathrm{89} \\ $$$${x}>\mathrm{10} \\ $$$${y}>\mathrm{20} \\ $$$${z}>\mathrm{2} \\ $$ Commented by redmiiuser…
Question Number 84002 by M±th+et£s last updated on 08/Mar/20 $$\frac{{sin}\left({x}\right)}{\:\sqrt{\mathrm{2}{sin}^{\mathrm{2}} \left({x}\right)+{cos}^{\mathrm{2}} \left({x}\right)}}\:+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}={csc}\left({x}\right)\sqrt{\mathrm{2}{sin}^{\mathrm{2}} \left({x}\right)+{cos}^{\mathrm{2}} \left({x}\right)} \\ $$$${show}\:{that} \\ $$$${x}=\left\{\frac{\pi}{\mathrm{2}}+\mathrm{2}\pi{n}\right\}\:{and}\:{x}=\left\{{cos}^{−\mathrm{1}} \left(\sqrt{\mathrm{3}}\right)−\pi+\mathrm{2}\pi{n}\right\} \\ $$$${and}\:{x}=\left\{−{cos}^{−\mathrm{1}} \left(\sqrt{\mathrm{3}}\right)+\mathrm{2}\pi{n}\right\} \\ $$$$ \\…
Question Number 84005 by redmiiuser last updated on 08/Mar/20 $${find}\:{atleast}\:\mathrm{7}\:{solutions} \\ $$$${of}\:{the}\:{equation}. \\ $$$$\mathrm{900}{x}+\mathrm{7689}{y}=\mathrm{109876} \\ $$$${CAN}\:{ANYONE}\:{SOLVE} \\ $$$${THIS} \\ $$$${now}\:{lets}\:{find}\:\mathrm{7}\:{integral} \\ $$$${solutions} \\ $$ Commented…
Question Number 149516 by mathdanisur last updated on 05/Aug/21 $$\Omega\:=\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{3}} {\int}}\:\left(\sqrt{\left({x}\:+\:\mathrm{2}\right)^{\mathrm{2}} \:-\:\mathrm{8}{x}}\right)\:{dx}\:=\:? \\ $$ Answered by Ar Brandon last updated on 05/Aug/21 $$\:\:=\int_{\mathrm{0}} ^{\mathrm{3}}…
Question Number 149505 by mathdanisur last updated on 05/Aug/21 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{n}\:+\:\mathrm{3}}{\mathrm{n}\:+\:\mathrm{1}}\right)^{\mathrm{n}} =\:? \\ $$ Commented by EDWIN88 last updated on 06/Aug/21 $$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{n}+\mathrm{3}}{{n}+\mathrm{1}}\right)^{{n}} =\:{e}^{\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{n}+\mathrm{3}}{{n}+\mathrm{1}}−\mathrm{1}\right){n}}…