Question Number 21321 by Tinkutara last updated on 20/Sep/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{real}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\mathrm{4}{x}^{\mathrm{99}} \:+\:\mathrm{5}{x}^{\mathrm{98}} \:+\:\mathrm{4}{x}^{\mathrm{97}} \:+\:\mathrm{5}{x}^{\mathrm{96}} \:+ \\ $$$$…..\:+\:\mathrm{4}{x}\:+\:\mathrm{5}\:=\:\mathrm{0}\:\mathrm{is} \\ $$ Answered by dioph last updated…
Question Number 152394 by Olaf_Thorendsen last updated on 28/Aug/21 $$\mathrm{Le}\:\mathrm{spaghetti}\:\mathrm{de}\:\mathrm{Cyril}\:\mathrm{Lignac}. \\ $$$$ \\ $$$$\mathrm{Le}\:\mathrm{chef}\:\mathrm{Cyril}\:\mathrm{Lignac}\:\mathrm{pr}\acute {\mathrm{e}pare}\:\mathrm{des} \\ $$$$\mathrm{spaghettis}.\:\mathrm{Mais}\:\mathrm{au}\:\mathrm{moment}\:\mathrm{de}\:\mathrm{les} \\ $$$$\mathrm{plonger}\:\mathrm{dans}\:\mathrm{l}'\mathrm{eau},\:\mathrm{l}'\mathrm{un}\:\mathrm{tombe}\:\mathrm{par} \\ $$$$\mathrm{terre}\:\mathrm{et}\:\mathrm{se}\:\mathrm{casse}\:\mathrm{en}\:\mathrm{trois}\:\mathrm{morceaux}. \\ $$$$ \\ $$$$\mathrm{Le}\:\mathrm{chef}\:\mathrm{Lignac}\:\mathrm{se}\:\mathrm{demande}\:\mathrm{alors}…
Question Number 21319 by Tinkutara last updated on 20/Sep/17 $$\mathrm{If}\:{x},\:{y},\:{z}\:\mathrm{are}\:\mathrm{three}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{such} \\ $$$$\mathrm{that}\:{x}\:+\:{y}\:+\:{z}\:=\:\mathrm{4}\:\mathrm{and}\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{z}^{\mathrm{2}} \:=\:\mathrm{6}, \\ $$$$\mathrm{then} \\ $$$$\left(\mathrm{1}\right)\:\frac{\mathrm{2}}{\mathrm{3}}\:\leqslant\:{x},\:{y},\:{z}\:\leqslant\:\mathrm{2} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{0}\:\leqslant\:{x},\:{y},\:{z}\:\leqslant\:\mathrm{2} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{1}\:\leqslant\:{x},\:{y},\:{z}\:\leqslant\:\mathrm{3} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{2}\:\leqslant\:{x},\:{y},\:{z}\:\leqslant\:\mathrm{3}…
Question Number 152388 by ajfour last updated on 28/Aug/21 Commented by ajfour last updated on 28/Aug/21 $${Find}\:{the}\:{maximum}\:{speed}\:{u}, \\ $$$${that}\:{can}\:{be}\:{given}\:{to}\:{the}\:{solid} \\ $$$${ball},\:{so}\:{that}\:{it}\:{goes}\:{through}\:{the} \\ $$$${paraboloid}\:{ditch}\:{y}={x}^{\mathrm{2}} −{b}^{\mathrm{2}} \\…
Question Number 86855 by jagoll last updated on 01/Apr/20 $$\mathrm{If}\:\mathrm{a},\mathrm{b}\:,\mathrm{c}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{3}} +\mathrm{6x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{3}\:=\:\mathrm{0}\:.\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{equation}\:\mathrm{with}\:\mathrm{roots}\:\mathrm{a}+\mathrm{b}\:,\:\mathrm{b}+\mathrm{c}\:,\:\mathrm{a}+\mathrm{c}\:? \\ $$ Answered by john santu last updated on…
Question Number 86853 by M±th+et£s last updated on 01/Apr/20 $$\int\frac{{x}^{\mathrm{6}} −{x}^{\mathrm{3}} +\mathrm{2}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} −\mathrm{2}}{dx} \\ $$ Answered by MJS last updated on 01/Apr/20 $$\frac{{x}^{\mathrm{6}} −{x}^{\mathrm{3}}…
Question Number 21316 by Tinkutara last updated on 20/Sep/17 $$\mathrm{Let}\:{p}\:=\:\left({x}_{\mathrm{1}} \:−\:{x}_{\mathrm{2}} \right)^{\mathrm{2}} \:+\:\left({x}_{\mathrm{1}} \:−\:{x}_{\mathrm{3}} \right)^{\mathrm{2}} \:+\:….\:+ \\ $$$$\left({x}_{\mathrm{1}} \:−\:{x}_{\mathrm{6}} \right)^{\mathrm{2}} \:+\:\left({x}_{\mathrm{2}} \:−\:{x}_{\mathrm{3}} \right)^{\mathrm{2}} \:+\:\left({x}_{\mathrm{2}} \:−\:{x}_{\mathrm{4}}…
Question Number 152385 by imjagoll last updated on 28/Aug/21 $$\:\mathrm{4}−\mathrm{cosec}\:^{\mathrm{2}} \left(\mathrm{2x}\right)\geqslant\:\mathrm{0} \\ $$$$\:\mathrm{find}\:\mathrm{x} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 86850 by john santu last updated on 01/Apr/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \:\left(\sqrt[{\mathrm{4}\:\:}]{\left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)}\right)^{\mathrm{3}} } \\ $$ Commented by john santu last updated on 01/Apr/20 Answered…
Question Number 21315 by Tinkutara last updated on 20/Sep/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{real}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\sqrt[{\mathrm{4}}]{\mathrm{97}\:−\:{x}}\:+\:\sqrt[{\mathrm{4}}]{{x}}\:=\:\mathrm{5} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com