Question Number 151448 by mathdanisur last updated on 21/Aug/21 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\boldsymbol{\mathrm{A}}\mathrm{rtimetric}\:\mathrm{mean}\:\geqslant\:\boldsymbol{\mathrm{G}}\mathrm{eometric}\:\mathrm{mean} \\ $$$$\frac{\mathrm{a}\:+\:\mathrm{b}}{\mathrm{2}}\:\geqslant\:\sqrt{\mathrm{ab}} \\ $$ Commented by puissant last updated on 21/Aug/21 $$\forall\:\left({a},{b}\right)\in\mathbb{R}^{\mathrm{2}} ,…
Question Number 85902 by mr W last updated on 26/Mar/20 $${find}\:{the}\:{coefficients}\:{of}\:{x}^{\mathrm{2}} \:{and}\:{x}^{\mathrm{3}} \: \\ $$$${terms}\:{in}\:{the}\:{expansion}\:{of} \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{2}} \left(\mathrm{1}+\mathrm{3}{x}\right)^{\mathrm{3}} …\left(\mathrm{1}+\mathrm{100}{x}\right)^{\mathrm{100}} \\ $$ Commented by Serlea last…
Question Number 20368 by Tinkutara last updated on 26/Aug/17 $$\mathrm{If}\:\alpha\:\mathrm{is}\:\mathrm{a}\:\mathrm{real}\:\mathrm{root}\:\mathrm{of}\:\mathrm{2}{x}^{\mathrm{3}} \:−\:\mathrm{3}{x}^{\mathrm{2}} \:+\:\mathrm{6}{x}\:+\:\mathrm{6}\:=\:\mathrm{0}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\left[\alpha\right]\:\mathrm{where}\:\left[\centerdot\right]\:\mathrm{denotes}\:\mathrm{the} \\ $$$$\mathrm{greatest}\:\mathrm{integer}\:\mathrm{function}. \\ $$ Commented by ajfour last updated on 26/Aug/17…
Question Number 20372 by Tinkutara last updated on 26/Aug/17 $$\mathrm{The}\:\mathrm{two}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{an}\:\mathrm{equation}\:{x}^{\mathrm{3}} \:−\:\mathrm{9}{x}^{\mathrm{2}} \\ $$$$+\:\mathrm{14}{x}\:+\:\mathrm{24}\:=\:\mathrm{0}\:\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{3}\::\:\mathrm{2}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{roots}. \\ $$ Answered by $@ty@m last updated on 26/Aug/17 $$\alpha+\mathrm{3}\beta+\mathrm{2}\beta=\mathrm{9}\:\Rightarrow\alpha+\mathrm{5}\beta=\mathrm{9}−−\left(\mathrm{1}\right)…
Question Number 151436 by mathdanisur last updated on 21/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 20367 by Tinkutara last updated on 26/Aug/17 $$\mathrm{Let}\:{f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:+\:\mathrm{3}{x}^{\mathrm{2}} \:+\:\mathrm{9}{x}\:+\:\mathrm{6sin}{x},\:\mathrm{then} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation} \\ $$$$\frac{\mathrm{1}}{{x}\:−\:{f}\left(\mathrm{1}\right)}\:+\:\frac{\mathrm{2}}{{x}\:−\:{f}\left(\mathrm{2}\right)}\:+\:\frac{\mathrm{3}}{{x}\:−\:{f}\left(\mathrm{3}\right)}\:=\:\mathrm{0}. \\ $$ Answered by ajfour last updated…
Question Number 151435 by mathdanisur last updated on 21/Aug/21 Commented by peter frank last updated on 21/Aug/21 $$\mathrm{new}\:\:\mathrm{ID}\:\mathrm{but}\:\mathrm{same}\:\mathrm{guy}.\mathrm{mr}\:\mathrm{w}\:\:\mathrm{do}\:\mathrm{you}\:\mathrm{remember}? \\ $$ Commented by mr W last…
Question Number 151418 by mathdanisur last updated on 20/Aug/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{three}\:\mathrm{digits}: \\ $$$$\mathrm{49}^{\mathrm{303}} \:\centerdot\:\mathrm{3993}^{\mathrm{202}} \:\centerdot\:\mathrm{39}^{\mathrm{606}} \\ $$ Answered by Olaf_Thorendsen last updated on 21/Aug/21 $${x}\:=\:\mathrm{49}^{\mathrm{303}} .\mathrm{3993}^{\mathrm{202}}…
Question Number 85871 by M±th+et£s last updated on 25/Mar/20 Commented by Rio Michael last updated on 25/Mar/20 $$\mathrm{all}\:\mathrm{integers} \\ $$ Commented by mr W last…
Question Number 85864 by john santu last updated on 26/Mar/20 $${simplify}\:{the}\:{expression} \\ $$$$\sqrt{\mathrm{6}+\mathrm{2}\sqrt{\mathrm{8}\sqrt{\mathrm{3}}−\mathrm{10}}}\:−\:\sqrt{\mathrm{7}−\sqrt{\mathrm{3}}}\:\:{in} \\ $$$${the}\:{form}\:\sqrt{\sqrt{{a}}+{b}}\:? \\ $$ Answered by jagoll last updated on 26/Mar/20 $$\mathrm{by}\:\mathrm{trick}\:!\:…