Category: Algebra

Question Number 210142 by Abdullahrussell last updated on 01/Aug/24 Commented by Frix last updated on 02/Aug/24 $$\mathrm{I}\mathrm{think}\mathrm{there}\mathrm{is}\mathrm{only}\mathrm{one}“{\mathrm{nice}}^{″}\mathrm{solution}:$$$$x=\frac{3}{2}-\frac{\sqrt{11}}{2}\mathrm{i}y=\frac{3}{2}+\frac{\sqrt{11}}{2}\mathrm{i}z=3$$$$\Rightarrow x+y+z=6$$$$\mathrm{But}\mathrm{there}\mathrm{should}\mathrm{be}\mathrm{more}\mathrm{solutions}\mathrm{with}$$$${x}+{y}+{z}\in\mathbb{R}…

Question Number 210155 by Spillover last updated on 01/Aug/24 Answered by A5T last updated on 01/Aug/24 Commented by A5T last updated on 01/Aug/24 $${C}\:{is}\:{the}\:{origin}\:{and}\:{redundant} \…

Question Number 210126 by mnjuly1970 last updated on 31/Jul/24 Answered by Frix last updated on 31/Jul/24 $$\mathrm{These}\mathrm{substitutions}\mathrm{make}\mathrm{it}\mathrm{easy}\mathrm{to}\mathrm{see}$$$${\mathrm{what}}^{\prime }\mathrm{s}\mathrm{going}\mathrm{on}:$$$$$$$$\mathrm{Let}\:{x}=\mathrm{sin}\:\alpha\:\overset{\left[\mathrm{differentiate}\right]} {\Rightarrow} \…

Question Number 210127 by essaad last updated on 31/Jul/24 Answered by lepuissantcedricjunior last updated on 01/Aug/24 $$\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{{x}}\right)−\boldsymbol{{lnx}}}{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}=\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{{x}}\right)}{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}−\int_{\mathrm{0}} ^{\mathrm{2}} \frac{\boldsymbol{{lnx}}}{\boldsymbol{{x}}^{\mathrm{2}}…

Question Number 210079 by Spillover last updated on 30/Jul/24 $$Finddirectionalderivatives\left(D_v\right)of$$$$f(x,y,z)=3{xy}^3-2{xz}^{2}inthedirectionofthe$$$$v=2i-3j+6k.$$$$thenEvaluatedirectionalderivatives$$$$atthepoint(3,1,-2)$$ Terms of…