Question Number 14491 by kailash2177mahto@gmail.com last updated on 01/Jun/17 $$\sqrt{\mathrm{25}} \\ $$$$ \\ $$ Answered by FilupS last updated on 01/Jun/17 $$\mathrm{25}=\left(\pm\mathrm{5}\right)^{\mathrm{2}} \\ $$$$\sqrt{\mathrm{25}}=\sqrt{\left(\pm\mathrm{5}\right)^{\mathrm{2}} }=\pm\mathrm{5}…
Question Number 14483 by chux last updated on 01/Jun/17 $$\mathrm{x}^{\mathrm{y}} +\mathrm{y}^{\mathrm{x}} =\mathrm{3}…..\left(\mathrm{1}\right) \\ $$$$\mathrm{x}+\mathrm{y}=\mathrm{3}…..\left(\mathrm{2}\right) \\ $$$$ \\ $$$$\mathrm{solve}\:\mathrm{the}\:\mathrm{equation} \\ $$ Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated…
Question Number 145548 by mathdanisur last updated on 05/Jul/21 $${if}\:\:\mathrm{3}^{\boldsymbol{{x}}} =\mathrm{24}\:\:{and}\:\:\mathrm{2}^{\boldsymbol{{y}}} =\mathrm{36} \\ $$$${find}\:\:\:\frac{\mathrm{4}^{\left(\boldsymbol{{x}}-\mathrm{1}\right)\centerdot\boldsymbol{{y}}} }{\mathrm{4}^{\boldsymbol{{x}}} }\:=\:? \\ $$ Answered by Ar Brandon last updated on…
Question Number 80004 by jagoll last updated on 30/Jan/20 $${x}\:{and}\:{y}\:{any}\:{integer}\:{satisfy} \\ $$$${equation}\:\left({x}−\mathrm{2004}\right)\left({x}−\mathrm{2006}\right)=\mathrm{2}^{{y}} \\ $$$${the}\:{greatest}\:{possible}\:{value} \\ $$$${of}\:{x}+{y} \\ $$ Commented by jagoll last updated on 30/Jan/20…
Question Number 79998 by john santu last updated on 30/Jan/20 $$\mathrm{given}\:\mathrm{3x}\:+\:\mathrm{4y}+\mathrm{1}\:=\:\mathrm{3}\sqrt{\mathrm{x}}\:+\:\mathrm{2}\sqrt{\mathrm{y}}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\sqrt{\mathrm{x}.\mathrm{y}}\: \\ $$ Commented by jagoll last updated on 30/Jan/20 Commented by john…
Question Number 145531 by mathdanisur last updated on 05/Jul/21 $$\underset{{n}\rightarrow\infty} {{lim}sin}^{\mathrm{2}} \pi\:\sqrt{{n}^{\mathrm{2}} +{n}}\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 05/Jul/21 $$\mathrm{sin}^{\mathrm{2}} \pi\sqrt{{n}^{\mathrm{2}} +{n}}\:=\:\mathrm{sin}^{\mathrm{2}}…
Question Number 145525 by mathdanisur last updated on 05/Jul/21 Answered by Olaf_Thorendsen last updated on 05/Jul/21 $${f}\left({x}+\mathrm{2}\right)+\mathrm{10}{f}\left({x}\right)\:=\:\mathrm{7}{f}\left({x}+\mathrm{1}\right) \\ $$$${f}\left({x}+\mathrm{2}\right)−\mathrm{7}{f}\left({x}+\mathrm{1}\right)+\mathrm{10}{f}\left({x}\right)\:=\:\mathrm{0} \\ $$$${r}^{\mathrm{2}} −\mathrm{7}{r}+\mathrm{10}\:=\:\mathrm{0} \\ $$$$\left({r}−\mathrm{2}\right)\left({r}−\mathrm{5}\right)\:=\:\mathrm{0} \\…
Question Number 145530 by mathdanisur last updated on 05/Jul/21 $$\left(\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mid{a}\mid\:+\:\mid{b}\mid}{\mid{a}\:+\:{b}\mid}\right)_{\boldsymbol{{min}}} =\:? \\ $$ Answered by puissant last updated on 07/Jul/21 $$\mid\mathrm{a}+\mathrm{b}\mid\leqslant\mid\mathrm{a}\mid+\mid\mathrm{b}\mid\:\Rightarrow\:\frac{\mid\mathrm{a}\mid+\mid\mathrm{b}\mid}{\mid\mathrm{a}+\mathrm{b}\mid}\:\geqslant\mathrm{1} \\ $$$$\Rightarrow\:\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mid\mathrm{a}\mid+\mid\mathrm{b}\mid}{\mid\mathrm{a}+\mathrm{b}\mid}\right)\geqslant\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\mathrm{take}\:\mathrm{min}=\frac{\mathrm{3}}{\mathrm{2}}..…
Question Number 145522 by ArielVyny last updated on 05/Jul/21 $${montrer}\:{que}\:{l}'{ensemble}\:{des}\:{suites}\:{reelle}\:{qui} \\ $$$${verifie}\:{la}\:{relation}\:\forall{n}\in\mathbb{N} \\ $$$${aU}_{{n}+\mathrm{2}} +{bU}_{{n}+\mathrm{1}} +{cU}_{{n}} =\mathrm{0}\:\left(\mathrm{1}\right)\:\:{est}\:{un}\:{espace} \\ $$$${vectoriel}\:{de}\:{dimension}\:\mathrm{2} \\ $$$${et}\:{determiner}\:{une}\:{base}\: \\ $$$$ \\ $$…
Question Number 79978 by mr W last updated on 29/Jan/20 $${Given}\:{for}\:{x},{y},{z}>\mathrm{0}: \\ $$$$\mathrm{2}^{{x}} =\mathrm{3}^{{y}} =\mathrm{5}^{{z}} \\ $$$${Arrange}\:\mathrm{2}{x},\:\mathrm{3}{y},\:\mathrm{5}{z}\:{in}\:{increasing}\:{order}. \\ $$ Answered by mind is power last…