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Category: Algebra

a-m-a-n-m-n-

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}}…

find-the-cube-root-of-9ab-2-b-2-24a-2-b-2-3a-2-

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…

x-2-2-2-1-2-y-2-2-2-3-2-z-2-2-2-5-2-w-2-2-2-7-2-1-x-2-4-2-1-2-y-2-4-2-3-2-z-2-4-2-5-2-w-2-4-2-7-2-1-x-2-6-2-1-2-y-2-6-2-3-2-z-2-

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} \\…