Question Number 167860 by infinityaction last updated on 27/Mar/22 Commented by infinityaction last updated on 27/Mar/22 $${find}\:{the}\:{real}\:{roots}\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 167840 by mathlove last updated on 27/Mar/22 Commented by cortano1 last updated on 27/Mar/22 $$\:\:\begin{cases}{{f}\left({x}\right)=\mathrm{2}+\left({a}−\mathrm{1}\right){x}}\\{{g}\left({x}\right)=\mathrm{2}−\left({a}+\mathrm{1}\right){x}}\end{cases} \\ $$$$\:\:\:{f}\left({g}\left({x}\right)\right)−{g}\left({f}\left({x}\right)\right)={f}\left({a}−\mathrm{1}\right)+{g}\left({a}+\mathrm{1}\right) \\ $$$$\:\:\begin{cases}{{f}\left({g}\left({x}\right)\right)=\mathrm{2}+\left({a}−\mathrm{1}\right)\left\{\mathrm{2}−\left({a}+\mathrm{1}\right){x}\right\}}\\{{g}\left({f}\left({x}\right)\right)=\mathrm{2}−\left({a}+\mathrm{1}\right)\left\{\mathrm{2}+\left({a}−\mathrm{1}\right){x}\right\}}\end{cases} \\ $$$$\:\begin{cases}{{f}\left({g}\left({x}\right)\right)=\mathrm{2}{a}−\left({a}^{\mathrm{2}} −\mathrm{1}\right){x}}\\{{g}\left({f}\left({x}\right)\right)=−\mathrm{2}{a}−\left({a}^{\mathrm{2}} −\mathrm{1}\right){x}}\end{cases}…
Question Number 167839 by mathlove last updated on 27/Mar/22 Answered by mr W last updated on 27/Mar/22 $${say}\:{x}+{y}+{z}−\mathrm{3}={s}\: \\ $$$$\Rightarrow{x}+{y}+{z}−{s}=\mathrm{3} \\ $$$$\begin{bmatrix}{\frac{\mathrm{1}}{\mathrm{668}}}&{\frac{\mathrm{1}}{\mathrm{669}}}&{\frac{\mathrm{1}}{\mathrm{670}}}&{\mathrm{0}}\\{\frac{\mathrm{1}}{\mathrm{670}}}&{\frac{\mathrm{1}}{\mathrm{671}}}&{\frac{\mathrm{1}}{\mathrm{672}}}&{\mathrm{0}}\\{\frac{\mathrm{1}}{\mathrm{674}}}&{\frac{\mathrm{1}}{\mathrm{675}}}&{\frac{\mathrm{1}}{\mathrm{676}}}&{\mathrm{0}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{−\mathrm{1}}\end{bmatrix}\begin{pmatrix}{{x}}\\{{y}}\\{{z}}\\{{s}}\end{pmatrix}=\begin{pmatrix}{\mathrm{1}}\\{\mathrm{1}}\\{\mathrm{1}}\\{\mathrm{3}}\end{pmatrix} \\ $$$${s}=\begin{bmatrix}{\frac{\mathrm{1}}{\mathrm{668}}}&{\frac{\mathrm{1}}{\mathrm{669}}}&{\frac{\mathrm{1}}{\mathrm{670}}}&{\mathrm{1}}\\{\frac{\mathrm{1}}{\mathrm{670}}}&{\frac{\mathrm{1}}{\mathrm{671}}}&{\frac{\mathrm{1}}{\mathrm{672}}}&{\mathrm{1}}\\{\frac{\mathrm{1}}{\mathrm{674}}}&{\frac{\mathrm{1}}{\mathrm{675}}}&{\frac{\mathrm{1}}{\mathrm{676}}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{3}}\end{bmatrix}/\begin{bmatrix}{\frac{\mathrm{1}}{\mathrm{668}}}&{\frac{\mathrm{1}}{\mathrm{669}}}&{\frac{\mathrm{1}}{\mathrm{670}}}&{\mathrm{0}}\\{\frac{\mathrm{1}}{\mathrm{670}}}&{\frac{\mathrm{1}}{\mathrm{671}}}&{\frac{\mathrm{1}}{\mathrm{672}}}&{\mathrm{0}}\\{\frac{\mathrm{1}}{\mathrm{674}}}&{\frac{\mathrm{1}}{\mathrm{675}}}&{\frac{\mathrm{1}}{\mathrm{676}}}&{\mathrm{0}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{−\mathrm{1}}\end{bmatrix}=\mathrm{2012} \\…
Question Number 167821 by mathlove last updated on 26/Mar/22 Commented by dangduomg last updated on 26/Mar/22 $$\Rightarrow\:{E}\:=\:\left(\mathrm{4}^{\mathrm{1}/\mathrm{5}} \right)^{\left(\mathrm{5}^{\mathrm{1}/\mathrm{4}} \right)^{{E}} } \\ $$$$=\:\mathrm{4}^{\mathrm{1}/\mathrm{5}×\left(\mathrm{5}^{\mathrm{1}/\mathrm{4}} \right)^{{E}} } \\…
Question Number 102278 by I want to learn more last updated on 08/Jul/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{following}\:\mathrm{without} \\ $$$$\mathrm{actually}\:\mathrm{expand}. \\ $$$$\left(\mathrm{i}\right)\:\:\:\:\:\:\:\:\left(\mathrm{5}\:\:−\:\:\mathrm{3x}\right)^{\mathrm{10}} \\ $$$$\left(\mathrm{ii}\right)\:\:\:\:\:\:\:\:\left(\mathrm{5}\:\:+\:\:\mathrm{3x}\right)^{−\:\mathrm{10}} \\ $$ Commented by mr…
Question Number 167800 by cortano1 last updated on 25/Mar/22 $$\:\:\:\:\:\:\mathrm{5}^{\mathrm{2}{x}} \:=\:\mathrm{2}.\mathrm{10}^{{x}} −\mathrm{4}^{\mathrm{2}{x}} \: \\ $$$$\:\:\:\:\:\sqrt[{\left({x}+\mathrm{2}\right)^{−\mathrm{1}} }]{\left({x}−\mathrm{4}\right)^{{x}^{\mathrm{2}} +\mathrm{2}} }=?\: \\ $$ Commented by MJS_new last updated…
Question Number 167777 by infinityaction last updated on 24/Mar/22 Answered by Jamshidbek last updated on 26/Mar/22 $$\boldsymbol{\mathrm{Solution}}. \\ $$$$\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +\mathrm{z}^{\mathrm{3}} −\mathrm{3xy}=\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} −\left(\mathrm{xy}+\mathrm{yz}+\mathrm{xz}\right)\right)…
Question Number 167772 by mathlove last updated on 24/Mar/22 $${x}+\sqrt{{x}}=\mathrm{5} \\ $$$${x}+\frac{\mathrm{5}}{\:\sqrt{{x}}}=? \\ $$ Commented by mr W last updated on 24/Mar/22 $$\left(\sqrt{{x}}\right)^{\mathrm{2}} +\sqrt{{x}}−\mathrm{5}=\mathrm{0} \\…
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Question Number 36696 by kumar12513 last updated on 04/Jun/18 $${if}\:{y}={tan}^{−\mathrm{1}} {x}\:{show}\:{that} \\ $$$$\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}_{{n}+\mathrm{2}} +\mathrm{2}\left({n}+\mathrm{1}\right){xy}_{{n}+\mathrm{1}} +{n}\left({n}+\mathrm{1}\right){y}_{{n}} =\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact:…