Question Number 192803 by mokys last updated on 27/May/23 Commented by mokys last updated on 28/May/23 $$?????? \\ $$ Answered by MM42 last updated on…
Question Number 192797 by York12 last updated on 27/May/23 $$\boldsymbol{{If}}\:\boldsymbol{{x}}\:\&\:\boldsymbol{{y}}\:\boldsymbol{{are}}\:\boldsymbol{{both}}\:\boldsymbol{{positive}}\:\boldsymbol{{integers}}\:\boldsymbol{{then}} \\ $$$$\boldsymbol{{then}}\:\boldsymbol{{show}}\:\boldsymbol{{if}}\:\boldsymbol{{it}}\:\boldsymbol{{possiple}}\:\boldsymbol{{that}}\:\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}+\mathrm{1}\:\&\:\boldsymbol{{y}}^{\mathrm{2}} \:+\:\mathrm{4}\boldsymbol{{x}}\:+\:\mathrm{3}\:\boldsymbol{{be}}\:\boldsymbol{{both}}\: \\ $$$$\boldsymbol{{perfect}}\:\boldsymbol{{squares}}\:\boldsymbol{{simultaneously}}. \\ $$ Answered by witcher3 last updated on 27/May/23…
Question Number 127260 by bramlexs22 last updated on 28/Dec/20 $$\left({x}^{\mathrm{2}} −\mathrm{1}\right){y}''−\mathrm{2}{xy}'+\mathrm{2}{y}\:=\:\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} \\ $$ Answered by liberty last updated on 28/Dec/20 $${let}\:{y}\:=\:{xz}\:{for}\:{some}\:{z}={z}\left({x}\right) \\ $$$${y}'={xz}'+{z}\:\wedge\:{y}''={xz}''+\mathrm{2}{z}' \\…
Question Number 127261 by mohammad17 last updated on 28/Dec/20 $${for}\:{any}\:{complex}\:{number}\:{if}\:{im}\left({z}\right)>\mathrm{0} \\ $$$${then}\:{im}\left(\frac{\mathrm{1}}{{z}}\right)>\mathrm{0}\:\:\:\:{prove}\:{this}\:? \\ $$ Commented by mr W last updated on 28/Dec/20 $${wrong}! \\ $$$${if}\:{im}\left({z}\right)>\mathrm{0}\:{then}\:{im}\left(\frac{\mathrm{1}}{{z}}\right)<\mathrm{0}.…
Question Number 61724 by aliesam last updated on 07/Jun/19 $$\underset{{n}\geqslant\mathrm{0}} {\sum}{n}^{\mathrm{2}} {x}^{{n}} \\ $$$$ \\ $$ Commented by maxmathsup by imad last updated on 07/Jun/19…
Question Number 192793 by York12 last updated on 27/May/23 $$\boldsymbol{{x}}^{\mathrm{4}} +\boldsymbol{{x}}^{\mathrm{3}} +\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{x}}+\mathrm{1}=\boldsymbol{{y}}^{\mathrm{2}} \:\boldsymbol{{where}}\:\boldsymbol{{y}}\:\boldsymbol{{is}}\:\boldsymbol{{positive}}\:\boldsymbol{{integer}}\:\boldsymbol{{number}} \\ $$$$\boldsymbol{{then}}\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{positive}}\:\boldsymbol{{integal}}\:\boldsymbol{{values}}\:\boldsymbol{{of}}\:\left(\boldsymbol{{x}}\right) \\ $$$$\boldsymbol{{for}}\:\boldsymbol{{which}}\:\boldsymbol{{that}}\:\boldsymbol{{holds}} \\ $$ Answered by AST last updated…
Question Number 61721 by Mr X pcx last updated on 07/Jun/19 $${calculate}\:{A}\:=\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{{n}} \right){dx} \\ $$$${and}\:{B}\:=\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{{n}} \right){dx}\:\:{with} \\ $$$${n}\geqslant\mathrm{2}\:\:\left({n}\:{integr}\:{natural}\right) \\ $$ Terms…
Question Number 61719 by aliesam last updated on 06/Jun/19 $$\int\frac{{dx}}{\mathrm{2}+{sin}\left({x}\right)} \\ $$ Commented by maxmathsup by imad last updated on 07/Jun/19 $${let}\:{A}\:=\:\int\:\:\frac{{dx}}{\mathrm{2}+{sinx}}\:\Rightarrow{A}\:=_{{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}} \:\:\:\int\:\:\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }}\:\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}} }…
Question Number 192791 by Mastermind last updated on 27/May/23 $$\mathrm{If}\:\mathrm{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer},\:\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{2}^{\mathrm{n}} \Gamma\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right)\:=\:\mathrm{1}.\mathrm{3}.\mathrm{5}…\left(\mathrm{2n}−\mathrm{1}\right)\sqrt{\pi}. \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$ Answered by Mathspace last updated on…
Question Number 127250 by joki last updated on 28/Dec/20 $$\int\mathrm{sin}^{\mathrm{4}} \mathrm{x}\:\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 28/Dec/20 $$\int{sin}^{\mathrm{2}} {x}\left(\mathrm{1}−{cos}^{\mathrm{2}} {x}\right){dx} \\…