Category: Algebra

Question Number 212016 by Spillover last updated on 27/Sep/24 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 211987 by Spillover last updated on 26/Sep/24 Commented by MathematicalUser2357 last updated on 26/Sep/24 $$\mathrm{No}\mathrm{closed}\mathrm{forms}\mathrm{for}{\int }_0^{\pi /2}{x}^2(\frac{1}{\sqrt{\tan x}}-\sqrt{\tan x})dx.$$$$\mathrm{But}\mathrm{you}\mathrm{can}\mathrm{just}\mathrm{approximate}.$$ Commented…

Question Number 212006 by RojaTaniya last updated on 26/Sep/24 Answered by a.lgnaoui last updated on 26/Sep/24 $$\mathrm{posons}\mathbf{z}=\mathbf{x}+100$$$$\:\:\frac{\left(\boldsymbol{\mathrm{z}}−\mathrm{2}\right)^{\mathrm{5}} +\left(\boldsymbol{\mathrm{z}}+\mathrm{2}\right)^{\mathrm{5}} }{\left(\boldsymbol{\mathrm{z}}−\mathrm{1}\right)^{\mathrm{5}} +\left(\boldsymbol{\mathrm{z}}+\mathrm{1}\right)^{\mathrm{5}} }=\frac{\mathrm{2}\boldsymbol{\mathrm{z}}^{\mathrm{5}} +\mathrm{80}\boldsymbol{\mathrm{z}}^{\mathrm{3}} +\mathrm{160}\boldsymbol{\mathrm{z}}}{\mathrm{2}\boldsymbol{\mathrm{z}}^{\mathrm{5}}…

Question Number 211949 by Spillover last updated on 25/Sep/24 Answered by MathematicalUser2357 last updated on 26/Sep/24 $$\mathrm{Thanks}\mathrm{for}\mathrm{the}\mathrm{integration}\mathrm{idea}!$$$$\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{\mathrm{1}}{{x}}\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\mathrm{ln}\left(\frac{{ax}^{\mathrm{2}} +\sqrt{\mathrm{2}{a}}{x}+\mathrm{1}}{{ax}^{\mathrm{2}} −\sqrt{\mathrm{2}{a}}{x}+\mathrm{1}}\right){dx}=\mathrm{4}\pi\:\mathrm{cot}^{−\mathrm{1}} \sqrt{\frac{\sqrt{{a}^{\mathrm{2}} +\mathrm{1}}+\mathrm{1}}{{a}}}…

Question Number 211954 by RojaTaniya last updated on 25/Sep/24 $$x,yarerationalnumberswhere$$$$x\ne 0,y\ne 0,x\ne y,thenisit$$$$possible:x^5+y^5=2x^2{y}^2?$$ Answered by Frix last updated…