Question Number 63449 by minh2001 last updated on 04/Jul/19 $${Do}\:{you}\:{remember}\:{that} \\ $$$$\pi\approx\mathrm{3}.\mathrm{1415926535897932}\ddots \\ $$$$\mathrm{38462643383279502884}\ddots \\ $$$$\mathrm{197}… \\ $$ Commented by minh2001 last updated on 04/Jul/19…
Question Number 128942 by bramlexs22 last updated on 11/Jan/21 $$\:\mathrm{Given}\::\:\mathrm{3}{xf}\left(\frac{\mathrm{1}}{{x}}\right)+{f}\left({x}\right)=\mathrm{2}{x}+\mathrm{2}\: \\ $$$${and}\:{f}\left(\mathrm{3}\right),\:\mathrm{f}\left(\mathrm{9}\right)\:,\:\mathrm{f}\left(\mathrm{a}\right)\:\mathrm{three}\:\mathrm{first} \\ $$$$\mathrm{term}\:\mathrm{in}\:\mathrm{AP}\:\mathrm{respectively}.\:\mathrm{Find} \\ $$$$\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:?\: \\ $$ Answered by liberty last updated on 11/Jan/21…
Question Number 128932 by Koyoooo last updated on 11/Jan/21 Commented by mr W last updated on 11/Jan/21 $${question}\:{is}\:{wrong}! \\ $$$$−\mathrm{3}\leqslant\mathrm{2}{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +\mathrm{2}{a}−\mathrm{4}{b}\leqslant\mathrm{44} \\ $$ Commented…
Question Number 128918 by Koyoooo last updated on 11/Jan/21 Commented by MJS_new last updated on 11/Jan/21 $$\mathrm{not}\:\mathrm{true}. \\ $$$$\mathrm{i}.\mathrm{e}.\:{a}=\mathrm{0}\wedge{b}=−\mathrm{4}\:\Rightarrow\:\mathrm{result}\:\mathrm{is}\:\mathrm{32} \\ $$ Commented by mr W…
Question Number 63381 by minh2001 last updated on 03/Jul/19 $${solve}\:{for}\:{both}\:{x}\:{and}\:{n} \\ $$$${in}\:{equation}:\:{x}^{{n}} =\mathrm{216}\:{in}\:{all} \\ $$$${part}\:{of}\:{integer} \\ $$$$\mathscr{A}\:\underset{{n}=\mathrm{3}} {\overset{{x}=\mathrm{6}} {\left\{}}\right. \\ $$$$\mathscr{B}\underset{{n}=\mathrm{4}} {\overset{{x}=\mathrm{5}} {\left\{}}\right. \\ $$$$\mathscr{C}\underset{{n}=\mathrm{5}}…
Question Number 63383 by minh2001 last updated on 03/Jul/19 $${solve}\:{this}\:{equation}\:{in}\:{all}\: \\ $$$${part}\:{of}\:{complex}\:{number}: \\ $$$$\sqrt{\left({x}^{\mathrm{9}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}−\mathrm{6}\right)+\mathrm{4}}=\left({x}^{\mathrm{9}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}−\mathrm{6}\right)−\mathrm{16} \\ $$ Commented by MJS last updated…
Question Number 63373 by MJS last updated on 31/Jul/19 $$\mathrm{just}\:\mathrm{found}\:\mathrm{this}\:\mathrm{on}\:\mathrm{the}\:\mathrm{web} \\ $$$$\mathrm{I}\:\mathrm{thought}\:\mathrm{it}\:\mathrm{might}\:\mathrm{help}\:\mathrm{in}\:\mathrm{some}\:\mathrm{cases}\:\mathrm{where} \\ $$$$\mathrm{quartics}\:\mathrm{appear}\:\mathrm{i}.\mathrm{e}.\:\mathrm{Sir}\:\mathrm{Aifour}'\mathrm{s}\:\mathrm{geometric} \\ $$$$\mathrm{questions}.\:\mathrm{sometimes}\:\mathrm{we}\:\mathrm{know}\:\mathrm{the}\:\mathrm{nature}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{roots},\:\mathrm{but}\:\mathrm{how}\:\mathrm{to}\:\mathrm{use}\:\mathrm{this}\:\mathrm{information}? \\ $$$$ \\ $$$${ax}^{\mathrm{4}} +{bx}^{\mathrm{3}} +{cx}^{\mathrm{2}} +{dx}+{e}=\mathrm{0}…
Question Number 128903 by Engr_Jidda last updated on 11/Jan/21 $${solve}\:{the}\:{differential}\:{equation} \\ $$$$\frac{{dy}^{\mathrm{2}} }{{dx}^{\mathrm{2}\:} }+{y}=\mathrm{0} \\ $$ Answered by mindispower last updated on 11/Jan/21 $${X}^{\mathrm{2}} +\mathrm{1}=\mathrm{0}\Rightarrow{X}\in\left\{{i},−{i}\right\}…
Question Number 128850 by ruwedkabeh last updated on 10/Jan/21 $$\sqrt{{x}+\sqrt{\mathrm{4}{x}+\sqrt{\mathrm{16}{x}+\sqrt{\mathrm{64}{x}+…+\sqrt{\mathrm{4}^{\mathrm{2019}} {x}+\mathrm{3}}}}}}−\sqrt{{x}}=\mathrm{1} \\ $$$${x}=? \\ $$ Answered by mindispower last updated on 10/Jan/21 $$\Rightarrow\sqrt{\mathrm{4}{x}+……+\sqrt{\mathrm{4}^{\mathrm{2009}} {x}+\mathrm{3}}}=\mathrm{1}+\mathrm{2}\sqrt{{x}} \\…
Question Number 63291 by aliesam last updated on 02/Jul/19 $${find}\:{some}\:{of}\:{all}\:{real}\:{x}\:{such}\:{that} \\ $$$$ \\ $$$$\frac{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{15}{x}+\mathrm{17}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{12}}\:=\:\frac{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{16}{x}+\mathrm{18}}{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{13}} \\ $$ Commented by Prithwish sen last…