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Author: Tinku Tara

The-number-of-real-solutions-of-the-equation-4x-99-5x-98-4x-97-5x-96-4x-5-0-is-

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…

Le-spaghetti-de-Cyril-Lignac-Le-chef-Cyril-Lignac-pre-pare-des-spaghettis-Mais-au-moment-de-les-plonger-dans-l-eau-l-un-tombe-par-terre-et-se-casse-en-trois-morceaux-Le-chef-Lignac-se-demande-

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}…

If-x-y-z-are-three-real-numbers-such-that-x-y-z-4-and-x-2-y-2-z-2-6-then-1-2-3-x-y-z-2-2-0-x-y-z-2-3-1-x-y-z-3-4-2-x-y-z-3-

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-152388

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}} \\…

If-a-b-c-are-the-roots-of-the-equation-x-3-6x-2-4x-3-0-find-the-equation-with-roots-a-b-b-c-a-c-

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…

Let-p-x-1-x-2-2-x-1-x-3-2-x-1-x-6-2-x-2-x-3-2-x-2-x-4-2-x-2-x-6-2-x-5-x-6-2-1-i-lt-j-6-6-x-i-x-j-2-Th

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}}…