Question Number 191640 by vishal1234 last updated on 28/Apr/23 $${x}^{\mathrm{3}} −\mathrm{1}\:=\:\left({x}−\mathrm{1}\right)\:\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right) \\ $$$$\Rightarrow\:{x}\:=\:\mathrm{1}\:{and}\:{x}\:=\:\frac{−\mathrm{1}\pm\sqrt{\mathrm{3}}\:{i}}{\mathrm{2}} \\ $$$$\Rightarrow\:{w}\:=\:−\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\sqrt{\mathrm{3}}{i}\:}{\mathrm{2}}\:{and}\:{w}^{\mathrm{2}} \:=\:−\frac{\mathrm{1}}{\mathrm{2}}\:−\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:{i} \\ $$$$\Rightarrow\:{w}^{\mathrm{3}} \:=\:\mathrm{1} \\ $$$${similarly}\:{x}^{\mathrm{3}} \:+\:\mathrm{1}=\:\mathrm{0} \\ $$$$\Rightarrow\:{x}\:=\:−\mathrm{1}\:{and}\:{x}\:=−{w}^{\mathrm{2}}…
Question Number 126104 by Mathgreat last updated on 17/Dec/20 $$\frac{{a}+{b}}{{c}}\:+\:\frac{{b}+{c}}{{a}}\:+\frac{{a}+{c}}{{b}}\:\geqslant\:\mathrm{4}{a}−\mathrm{3}{b}+{c} \\ $$$${a}\geqslant{b}\geqslant{c} \\ $$ Commented by Mathgreat last updated on 17/Dec/20 $$\boldsymbol{{prove}} \\ $$ Terms…
Question Number 191642 by a.lgnaoui last updated on 30/Apr/23 $$\mathrm{Comparer}\:\left[\mathrm{OHDF}\right]\:\:\mathrm{avec}\:\left[\mathrm{ABHEF}\right] \\ $$$$\left({avec}\:{preuve}\right) \\ $$$$\:\:{Sa}\mathrm{c}{h}\mathrm{a}{nt}\:{que}: \\ $$$$\mathrm{OH}\mid\mid\mathrm{DF}\:\:\:\mathrm{HE}=\mathrm{EF}\:\:\:\mathrm{OB}=\mathrm{4OA} \\ $$$$\:\:\:\mathrm{CH}=\mathrm{2BC}\:\mathrm{et}\:\mathrm{BC}<\mathrm{OB}.\:\:\: \\ $$$$ \\ $$ Commented by a.lgnaoui…
Question Number 126105 by Mathgreat last updated on 17/Dec/20 $$\mathrm{1}\leqslant{a};{b};{c};{d}\leqslant\mathrm{2} \\ $$$$\mid\left(\mathrm{1}−{a}\right)\left(\mathrm{1}−{b}\right)\left(\mathrm{1}−{c}\right)\left(\mathrm{1}−{d}\right)\mid\leqslant\frac{{abcd}}{\mathrm{4}} \\ $$ Commented by Mathgreat last updated on 17/Dec/20 $$\boldsymbol{{prove}} \\ $$ Answered…
Question Number 191637 by Tawa11 last updated on 28/Apr/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 191639 by a.lgnaoui last updated on 28/Apr/23 $$\mathrm{Une}\:\mathrm{feuille}\:\mathrm{de}\:\mathrm{papier}\:\mathrm{format}\:\boldsymbol{\mathrm{A}}\mathrm{4}\:\mathrm{est}\:\mathrm{plie} \\ $$$$\:\boldsymbol{\mathrm{n}}\:\mathrm{fois}\:\mathrm{simultanement}\:\mathrm{en}\:\mathrm{longueur}\:\mathrm{et} \\ $$$$\mathrm{largeur}\:\left(\mathrm{total}\:\mathrm{plie}=\mathrm{2n}\right) \\ $$$$−\mathrm{Quel}\:\mathrm{son}\:\mathrm{les}\:\mathrm{nouvelles}\:\mathrm{dimensions}\:\mathrm{de}\:\mathrm{cette}\:\mathrm{feuille} \\ $$$$\:\:\:\mathrm{la}\:\mathrm{feuille}\:\mathrm{a}\:\mathrm{la}\:\mathrm{fin}\:. \\ $$$$−\mathrm{quel}\:\mathrm{seront}\:\mathrm{ses}\:\mathrm{dimensions}\:\:\mathrm{apres}\: \\ $$$$\:\:\:\:\mathrm{6}\:\boldsymbol{\mathrm{pliages}} \\ $$$$−\mathrm{Quel}\:\mathrm{seront}\:\:\mathrm{les}\:\mathrm{dimensions}\:\mathrm{pour}\:\mathrm{une}\:\mathrm{feuille}\:\boldsymbol{\mathrm{care}}\:\mathrm{de}\:\mathrm{30}\:\boldsymbol{\mathrm{cm}}\: \\…
Question Number 191633 by MikeH last updated on 27/Apr/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 126098 by ZiYangLee last updated on 17/Dec/20 $$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\mathrm{27}\left(\mathrm{sin}^{\mathrm{4}} \alpha+\mathrm{2cos}^{\mathrm{4}} \alpha\right)\geqslant\mathrm{16}\left(\mathrm{sin2}\alpha\right)^{\mathrm{2}} \\ $$ Answered by MJS_new last updated on 17/Dec/20 $$\mathrm{sin}\:\mathrm{2}\alpha\:=\mathrm{2sin}\:\alpha\:\mathrm{cos}\:\alpha \\…
Question Number 191632 by Spillover last updated on 27/Apr/23 $$\int_{\mathrm{0}} ^{\infty} \sqrt{\mathrm{tan}\:\theta}\:{d}\theta \\ $$ Commented by Tinku Tara last updated on 28/Apr/23 $$\mathrm{Q113706} \\ $$…
Question Number 126097 by amns last updated on 17/Dec/20 Commented by amns last updated on 17/Dec/20 $$\mathrm{I}\:\mathrm{need}\:\mathrm{someone}'\mathrm{s}\:\mathrm{help}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{it}!!! \\ $$ Answered by Dwaipayan Shikari last updated…