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Question Number 211753 by alcohol last updated on 19/Sep/24 $${find}\:{all}\:\left({n},{m}\right)\:{such}\:{that}\:\frac{{n}^{\mathrm{2}} −{m}}{{m}^{\mathrm{2}} −{n}}\:\in\:\mathbb{Z} \\ $$ Answered by Frix last updated on 20/Sep/24 $$\mathrm{There}\:\mathrm{are}\:\mathrm{infinitely}\:\mathrm{many}\:\mathrm{solutions}. \\ $$$$\mathrm{3}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{find}\:\mathrm{some}: \\…
Question Number 211738 by MrGaster last updated on 19/Sep/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{\mathrm{1}}{\boldsymbol{{x}}^{\mathrm{5}} +\mathrm{1}\:}\boldsymbol{{dx}}. \\ $$$$ \\ $$ Commented by Frix last updated on 19/Sep/24 $$=\int\frac{{dx}}{\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}}…
Question Number 211732 by BaliramKumar last updated on 19/Sep/24 Answered by TonyCWX08 last updated on 19/Sep/24 $${Using}\:{quadratic}\:{formula} \\ $$$${x}=\frac{{sin}^{\mathrm{2}} \theta\pm\sqrt{{sin}^{\mathrm{4}} \theta\:+\:\mathrm{4}{cos}^{\mathrm{2}} \theta}}{\mathrm{2}} \\ $$$$ \\…
Question Number 211749 by universe last updated on 19/Sep/24 $${volume}\:{bounded}\:{by}\:{the}\:{curve} \\ $$$$\:{z}\:=\:\sqrt{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} }\:\:\:{and}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\:\mathrm{6}^{\mathrm{2}} \\ $$ Answered by mr W last updated…
Question Number 211750 by Alijumaaxyz last updated on 19/Sep/24 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{a}^{\mathrm{1}/{x}} +{b}^{\mathrm{1}/{x}} }{\mathrm{2}}\right)^{{x}} ;\left({a},{b}\right)\in\mathbb{R}_{+} ^{\ast} \\ $$ Answered by mehdee7396 last updated on 19/Sep/24 $${li}\underset{{x}\rightarrow\infty}…
Question Number 211734 by BaliramKumar last updated on 19/Sep/24 Answered by TonyCWX08 last updated on 19/Sep/24 $${y}={kx}\:\Rightarrow\:{k}=\frac{{y}}{{x}} \\ $$$${z}={ky}\:\Rightarrow\:{k}=\frac{{z}}{{y}} \\ $$$$\frac{{y}}{{x}}=\frac{{z}}{{y}} \\ $$$${y}^{\mathrm{2}} ={xy}\:=\:{B} \\…
Question Number 211745 by Majak last updated on 19/Sep/24 $$\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\left(\mathrm{10}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{20}\right) \\ $$ Commented by Majak last updated on 19/Sep/24 $${need}\:{help}\:{guy} \\ $$ Answered…
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