Category: Algebra

Question Number 154015 by mathdanisur last updated on 13/Sep/21 $$\mathrm{If}\mathrm{x};\mathrm{y};\mathrm{z}>0\mathrm{then}\mathrm{prove}\mathrm{that}:$$$$\frac{\mathrm{x}}{{\mathrm{x}}^2+\mathrm{yz}}+\frac{\mathrm{y}}{{\mathrm{y}}^2+\mathrm{zx}}+\frac{\mathrm{z}}{{\mathrm{z}}^2+\mathrm{xy}}⩽\frac{{\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2}{2\mathrm{xyz}}$$ Terms of Service Privacy Policy…

Question Number 88458 by TawaTawa1 last updated on 10/Apr/20 $$\mathrm{Using}\mathrm{the}\mathrm{principle}\mathrm{of}\mathrm{mathematical}\mathrm{induction}\mathrm{to}\mathrm{prove}$$$$\mathrm{that}{\mathrm{a}}_1,{\mathrm{a}}_2,\dots ,{\mathrm{a}}_{\mathrm{n}},\frac{{\mathrm{a}}_1+{\mathrm{a}}_2+\dots +{\mathrm{a}}_{\mathrm{n}}}{\mathrm{n}}⩾\sqrt[\mathrm{n}]{{\mathrm{a}}_1,{\mathrm{a}}_2,\dots ,{\mathrm{a}}_{\mathrm{n}}}$$ Terms of…

Question Number 153989 by mathdanisur last updated on 12/Sep/21 $$\mathrm{find}\mathrm{all}\mathrm{functions}\mathrm{f}:\mathbb{R}\to \mathbb{R}\mathrm{with}\mathrm{the}$$$$\mathrm{property}\mathrm{that}$$$$\mathrm{f}(\mathrm{f}\left(\mathrm{x}\right)+2\mathrm{y}=10\mathrm{x}+\mathrm{f}(\mathrm{f}\left(\mathrm{y}\right)-3\mathrm{x})$$$$\mathrm{holds}\mathrm{for}\mathrm{all}\mathrm{a};\mathrm{b}\in \mathbb{R}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 22856 by FilupS last updated on 23/Oct/17 $$\mathrm{solve}:\sin \left(x\right)=2,x\in \mathbb{C}$$ Commented by Tinkutara last updated on 23/Oct/17 $$Writeas{e}^{i\theta }=\cos \theta +i\sin \theta and$$$${e}^{−{i}\theta} =\mathrm{cos}\:\theta−{i}\mathrm{sin}\:\theta \…

Question Number 88372 by mr W last updated on 10/Apr/20 $$Therearefourboxes,eachofthem$$$$containsexactlythesamenumbers:$$$$1,2,3,\dots ,n.$$$$Fourdifferentnumbersaredrawn$$$$fromtheboxesandmultiplicated$$$$witheachothertogetaproduct.$$$${What}^{\prime }sthesumofallproducts?$$$$\underset{{a}\neq{b}\neq{c}\neq{d}}…