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 $$\mathrm{by}\:\mathrm{trick}\:!\:…
Question Number 151393 by Tawa11 last updated on 20/Aug/21 Answered by mr W last updated on 20/Aug/21 $$\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +…\right)^{\mathrm{3}} \left(\mathrm{1}+{x}^{\mathrm{5}} +{x}^{\mathrm{10}} +{x}^{\mathrm{15}} +…\right) \\ $$$$=\left(\mathrm{1}+{x}^{\mathrm{5}}…
Question Number 85854 by jagoll last updated on 25/Mar/20 $$\mathrm{If}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\in\:\mathbb{R}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:+\:\mathrm{z}^{\mathrm{4}} \:=\:\mathrm{4xyz}\:−\mathrm{1}\: \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\: \\ $$ Commented by mr W…
Question Number 151391 by mathdanisur last updated on 20/Aug/21 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b}\in\mathbb{R}\:\:\mathrm{and} \\ $$$$\left(\mathrm{a}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{b}^{\mathrm{2}} +\mathrm{1}\right)+\mathrm{9}=\mathrm{6}\left(\mathrm{a}+\mathrm{b}\right) \\ $$$$\mathrm{find}\:\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} =? \\ $$ Answered by dumitrel last updated…
Question Number 151383 by mathdanisur last updated on 20/Aug/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y}>\mathrm{0}\:\:\mathrm{peove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{2}}{\mathrm{3}}\:\centerdot\:\frac{\mathrm{2}}{\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{y}}}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\:\centerdot\:\sqrt{\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }{\mathrm{2}}}\:\geqslant\:\mathrm{xy} \\ $$ Commented by mathdanisur last updated on 20/Aug/21 $$\mathrm{Thank}\:\mathrm{You}\:\mathrm{Dear}\:\boldsymbol{\mathrm{S}}\mathrm{er},\:\geqslant\sqrt[{\mathrm{3}}]{\mathrm{xy}}\:\mathrm{for}\:\mathrm{solution}\:\mathrm{please} \\…