Question Number 128457 by SLVR last updated on 07/Jan/21 Commented by BHOOPENDRA last updated on 07/Jan/21 $${x}^{\mathrm{5}} =\frac{\mathrm{133}{x}−\mathrm{78}}{\mathrm{133}−\mathrm{78}{x}} \\ $$$$\mathrm{78}{x}^{\mathrm{6}} −\mathrm{133}{x}^{\mathrm{5}} +\mathrm{133}−\mathrm{78}=\mathrm{0} \\ $$$$\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{78}{x}^{\mathrm{4}}…
Question Number 62895 by Tawa1 last updated on 26/Jun/19 Commented by Tony Lin last updated on 26/Jun/19 $${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\frac{\mathrm{5}}{\mathrm{2}} \\ $$$$\Rightarrow{a}=\pm\sqrt{\frac{\mathrm{1}}{\mathrm{2}}},\:{b}=\pm\sqrt{\frac{\mathrm{1}}{\mathrm{2}}},\:{c}=\pm\sqrt{\frac{\mathrm{3}}{\mathrm{2}}} \\ $$$$\because\:\mid{ab}\mid<\mid{bc}\mid=\mid{ac}\mid…
Question Number 128388 by enter last updated on 06/Jan/21 $${y}=−{sin}\left(\frac{\Pi}{\mathrm{2}}+\mathrm{2}{x}\right)+\mathrm{2}{cos}\left(\mathrm{5}{x}+\Pi\right) \\ $$$${y}_{{min}} =\:?? \\ $$ Commented by TheSupreme last updated on 07/Jan/21 $${y}=−{cos}\left(\mathrm{2}{x}\right)−\mathrm{2}{cos}\left(\mathrm{5}{x}\right)\geqslant−\mathrm{3} \\ $$$${y}=−\mathrm{3}\:{x}=\mathrm{10}{k}\pi…
Question Number 62844 by alphaprime last updated on 25/Jun/19 $${Let}\:{p}\left({x}\right)\:=\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:\:{be}\:{such}\:{that}\:{p}\left({x}\right)\:{takes}\:{real}\:{values} \\ $$$${for}\:{real}\:{values}\:{of}\:{x}\:{and}\:{non}−{real}\:{values}\:{for}\:{non}−{real} \\ $$$${values}\:{of}\:{x}\:.\:{Prove}\:{that}\:{a}\:=\:\mathrm{0}\:{and}\:{find}\:{all} \\ $$$${possible}\:{values}\:{of}\:{c}. \\ $$ Answered by ajfour last updated on…
Question Number 128371 by aliibrahim1 last updated on 06/Jan/21 Commented by MJS_new last updated on 06/Jan/21 $${A}_{{n}} =\frac{\mathrm{752}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{2}{k}−\mathrm{1}}\:−\mathrm{752}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{2}{k}}}{\mathrm{2}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{n}+{k}}} \\…
Question Number 128368 by I want to learn more last updated on 06/Jan/21 $$\mathrm{If}\:\:\:\:\mathrm{a}_{\mathrm{1}} \:=\:\:\mathrm{2},\:\:\:\:\mathrm{a}_{\mathrm{2}} \:\:=\:\:\mathrm{3},\:\:\:\:\:\:\mathrm{a}_{\mathrm{n}\:\:+\:\:\mathrm{2}} \:\:=\:\:\mathrm{a}_{\mathrm{n}\:\:+\:\:\mathrm{1}} \:\:+\:\:\frac{\mathrm{a}}{\mathrm{2}},\:\:\:\:\:\:\mathrm{find}\:\:\mathrm{a}_{\mathrm{n}} \\ $$ Answered by mr W last…
Question Number 128369 by I want to learn more last updated on 06/Jan/21 $$\mathrm{If}\:\:\:\mathrm{u}_{\mathrm{1}} \:\:+\:\:\mathrm{u}_{\mathrm{2}} \:\:+\:\:\mathrm{u}_{\mathrm{3}} \:\:+\:\:…\:\:+\:\:\mathrm{u}_{\mathrm{n}} \:\:\:=\:\:\:\mathrm{2n}^{\mathrm{2}} \:\:+\:\:\mathrm{n}\:\:\:\mathrm{is}\:\mathrm{an}\:\mathrm{AP}. \\ $$$$\mathrm{Find}\:\:\:\:\:\:\:\:\mathrm{u}_{\mathrm{1}} \:\:+\:\:\mathrm{u}_{\mathrm{2}} \:\:+\:\:\mathrm{u}_{\mathrm{3}} \:\:+\:\:…\:\:+\:\:\mathrm{u}_{\mathrm{2n}\:\:−\:\:\mathrm{2}} \:\:+\:\:\mathrm{u}_{\mathrm{2n}\:\:−\:\:\mathrm{1}}…
Question Number 128341 by liberty last updated on 06/Jan/21 $$\mathrm{Which}\:\mathrm{is}\:\mathrm{larger}\:\mathrm{Z}\:=\:\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{3}}{\mathrm{6}−\frac{\mathrm{4}}{\mathrm{11}}}}\:\mathrm{or}\:\mathrm{S}\:=\:\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{3}}{\mathrm{6}−\frac{\mathrm{5}}{\mathrm{11}}}}\:? \\ $$ Commented by mr W last updated on 06/Jan/21 $${without}\:{calculation}: \\ $$$${Z}:\:{larger}\nearrow{smaller}\nearrow{larger} \\ $$$$\Rightarrow{Z}\:{is}\:{larger}\:{than}\:{S}.…
Question Number 62798 by ANTARES VY last updated on 25/Jun/19 $$\boldsymbol{\mathrm{Calculate}} \\ $$$$\boldsymbol{\mathrm{tg}}\left(\mathrm{20}°\right)+\mathrm{4}\boldsymbol{\mathrm{sin}}\left(\mathrm{20}°\right)+\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128329 by bramlexs22 last updated on 06/Jan/21 $$\left(\mathrm{2}\right)\mathrm{Solution}\:\mathrm{set}\::\:{x}\:\mid\mathrm{2}{x}−\mathrm{6}\:\mid\:<\:\mathrm{3}{x}\: \\ $$$$\mathrm{is}\:\_ \\ $$$$\left(\mathrm{2}\right)\:\mathrm{If}\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\mathrm{2}−\sqrt{{a}+{bx}^{\mathrm{3}} }}{{x}−\mathrm{2}}\:=\:{H}\:,\:{then} \\ $$$$\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}} −\mathrm{4}}{\:\sqrt{{a}+{bx}^{\mathrm{3}} }−\mathrm{1}}\:=\:\_ \\ $$ Answered by…