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Category: Algebra

s-a-b-c-d-number-terms-n-a-b-c-d-gt-0-then-E-s-s-a-s-s-b-s-s-c-a-E-gt-n-2-b-E-gt-n-2-n-1-c-E-gt-n-n-1-d-E-gt-n-2-n-1-e-E-gt-n-2-1-

Question Number 193238 by lmcp1203 last updated on 08/Jun/23 $${s}={a}+{b}+{c}+{d}+….. \\ $$$${number}\:{terms}\::{n} \\ $$$$\left\{{a};{b};{c};{d}…..\right\}>\mathrm{0} \\ $$$$\left.{then}\:{E}={s}/\left({s}−{a}\right)+{s}/\left({s}−{b}\right)+{s}/{s}−{c}\right)+…. \\ $$$$\left.{a}\left.\right)\:{E}>={n}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:{b}\right){E}>={n}^{\mathrm{2}} /\left({n}−\mathrm{1}\right) \\ $$$$\left.{c}\left.\right)\:{E}>={n}/\left({n}+\mathrm{1}\right)\:\:\:\:\:\:{d}\right)\:{E}>={n}^{\mathrm{2}} /\left({n}+\mathrm{1}\right) \\ $$$$\left.{e}\right)\:{E}>={n}^{\mathrm{2}}…

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Question Number 193213 by simplifiedmaths965 last updated on 07/Jun/23 $$\left(\frac{{a}^{{m}} }{{a}^{−{n}} }\right)^{{m}−{n}} \\ $$ Answered by aba last updated on 07/Jun/23 $$\left(\frac{\mathrm{a}^{\mathrm{m}} }{\mathrm{a}^{−\mathrm{n}} }\right)^{\mathrm{m}−\mathrm{n}} =\left(\mathrm{a}^{\mathrm{m}+\mathrm{n}}…

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Question Number 193221 by York12 last updated on 07/Jun/23 $$ \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{cube}}\:\boldsymbol{{root}}\:\boldsymbol{{of}} \\ $$$$\mathrm{9}\boldsymbol{{ab}}^{\mathrm{2}} \:+\:\left(\boldsymbol{{b}}^{\mathrm{2}} +\mathrm{24}\boldsymbol{{a}}^{\mathrm{2}} \right)\sqrt{\boldsymbol{{b}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{{a}}^{\mathrm{2}} } \\ $$ Answered by som(math1967) last…

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Question Number 193182 by York12 last updated on 06/Jun/23 $$ \\ $$$$\frac{{x}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} }+\frac{{z}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{5}^{\mathrm{2}} }+\frac{{w}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }=\mathrm{1} \\…

Question-131064

Question Number 131064 by shaker last updated on 01/Feb/21 Answered by Dwaipayan Shikari last updated on 01/Feb/21 $$\frac{\mathrm{1}}{\mathrm{4}}\int\frac{\mathrm{1}}{{x}}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }−\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{4}}\right){dx} \\ $$$$=−\frac{\mathrm{1}}{\mathrm{8}{x}^{\mathrm{2}} }−\frac{\mathrm{1}}{\mathrm{16}}\int\frac{\mathrm{1}}{{x}}−\frac{{x}}{{x}^{\mathrm{2}} +\mathrm{4}}{dx} \\…

a-b-b-a-b-3-b-a-a-a-b-2-a-b-R-

Question Number 65495 by behi83417@gmail.com last updated on 30/Jul/19 $$\begin{cases}{\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{b}}}+\frac{\boldsymbol{\mathrm{b}}}{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}}=\sqrt{\mathrm{3}}}\\{\frac{\boldsymbol{\mathrm{b}}}{\boldsymbol{\mathrm{a}}}+\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}}=\sqrt{\mathrm{2}}}\end{cases}\:\:\:\left[\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\boldsymbol{\mathrm{R}}\right] \\ $$ Answered by MJS last updated on 31/Jul/19 $${b}={at} \\ $$$$\begin{cases}{\frac{{t}^{\mathrm{2}} +{t}+\mathrm{1}}{{t}\left({t}+\mathrm{1}\right)}=\sqrt{\mathrm{3}}}\\{\frac{{t}^{\mathrm{2}} +{t}+\mathrm{1}}{{t}+\mathrm{1}}=\sqrt{\mathrm{2}}}\end{cases} \\…