Menu Close

Category: Algebra

I-want-to-make-cyllinders-of-maximum-volume-V-max-with-minimum-surface-area-S-min-because-they-are-more-profitable-for-me-I-need-the-help-of-mathematicians-of-this-forum-

Question Number 3996 by Rasheed Soomro last updated on 26/Dec/15 $${I}\:{want}\:{to}\:{make}\:{cyllinders}\:{of}\:\boldsymbol{{maximum}} \\ $$$$\boldsymbol{{volume}}\:\boldsymbol{\mathrm{V}}_{\boldsymbol{\mathrm{max}}} \:{with}\:{minimum}\:\boldsymbol{{surface}}\:\boldsymbol{{area}}\: \\ $$$$\boldsymbol{\mathrm{S}}_{\boldsymbol{\mathrm{min}}} \:,{because}\:{they}\:{are}\:{more}\:{profitable}\:{for}\:{me}. \\ $$$${I}\:{need}\:{the}\:{help}\:{of}\:{mathematicians}\:{of}\:{this} \\ $$$${forum}. \\ $$$$ \\ $$…

Are-there-more-Trancendental-or-Non-Trancendental-numbers-NOTE-Trancendentals-are-numbers-that-cannot-be-written-algerbraically-e-g-x-2-2-2-is-non-trancendental-pi-is-transendental-

Question Number 3994 by Filup last updated on 26/Dec/15 $$\mathcal{A}\mathrm{re}\:\mathrm{there}\:\mathrm{more}\:\:\mathcal{T}{rancendental} \\ $$$${or}\:\mathcal{N}{on}-\mathcal{T}{rancendental}\:{numbers}? \\ $$$$ \\ $$$$\mathcal{NOTE}: \\ $$$$\mathcal{T}{rancendentals}\:{are}\:{numbers}\:{that} \\ $$$${cannot}\:{be}\:{written}\:{algerbraically}. \\ $$$$ \\ $$$${e}.{g}.\:{x}^{\mathrm{2}} =\mathrm{2}…

to-Sir-Aifour-we-can-construct-polynomes-of-both-3-rd-and-4-th-degree-in-a-way-that-the-constants-are-Z-or-Q-and-the-solutions-are-not-trivial-i-e-t-t-2-t-2-0-t-x-

Question Number 69479 by MJS last updated on 24/Sep/19 $$\mathrm{to}\:\mathrm{Sir}\:\mathrm{Aifour}: \\ $$$$\mathrm{we}\:\mathrm{can}\:\mathrm{construct}\:\mathrm{polynomes}\:\mathrm{of}\:\mathrm{both}\:\mathrm{3}^{\mathrm{rd}} \:\mathrm{and} \\ $$$$\mathrm{4}^{\mathrm{th}} \:\mathrm{degree}\:\mathrm{in}\:\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{the}\:\mathrm{constants}\:\mathrm{are} \\ $$$$\in\mathbb{Z}\:\mathrm{or}\:\in\mathbb{Q}\:\mathrm{and}\:\mathrm{the}\:\mathrm{solutions}\:\mathrm{are}\:\mathrm{not}\:\mathrm{trivial} \\ $$$$\mathrm{i}.\mathrm{e}. \\ $$$$\left({t}−\alpha\right)\left({t}+\frac{\alpha}{\mathrm{2}}−\sqrt{\beta}\right)\left({t}+\frac{\alpha}{\mathrm{2}}+\sqrt{\beta}\right)=\mathrm{0}\wedge{t}={x}+\frac{\gamma}{\mathrm{3}} \\ $$$$\Leftrightarrow \\…

a-1-b-1-c-1-2abc-a-b-c-N-

Question Number 134981 by oooooooo last updated on 09/Mar/21 $$\left(\mathrm{a}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{b}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{c}}+\mathrm{1}\right)=\mathrm{2}\boldsymbol{\mathrm{abc}}\: \\ $$$$\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{c}}\:\varepsilon\:\mathrm{N} \\ $$ Answered by MJS_new last updated on 10/Mar/21 $$\mathrm{let}\:{a}\leqslant{b}\leqslant{c} \\ $$$$\left(\mathrm{1}\right)\:{c}=\left({a}+\mathrm{1}\right)\left({b}+\mathrm{1}\right) \\…