Question Number 23250 by Tinkutara last updated on 28/Oct/17 $${If}\:\left(\mathrm{1}\:+\:{x}\right)^{{n}} \:=\:{C}_{\mathrm{0}} \:+\:{C}_{\mathrm{1}} {x}\:+\:{C}_{\mathrm{2}} {x}^{\mathrm{2}} \:+\:{C}_{\mathrm{3}} {x}^{\mathrm{3}} \\ $$$$+\:…\:+\:{C}_{{n}} {x}^{{n}} ,\:{then}\:{prove}\:{that} \\ $$$$\underset{\mathrm{0}\leqslant{i}<{j}\leqslant{n}} {\Sigma\Sigma}\left(\frac{{i}}{\:^{{n}} {C}_{{i}} }\:+\:\frac{{j}}{\:^{{n}}…
Question Number 88771 by M±th+et£s last updated on 12/Apr/20 $${solve} \\ $$$${x}^{{x}^{\mathrm{4}} } =\mathrm{64} \\ $$ Commented by mr W last updated on 12/Apr/20 $${x}^{{x}^{\mathrm{4}}…
Question Number 154303 by mathdanisur last updated on 16/Sep/21 $$\mathrm{Solve}\:\mathrm{in}\:\mathbb{R} \\ $$$$\frac{\mathrm{z}^{\mathrm{9}} \:-\:\mathrm{81z}\:-\:\mathrm{62}}{\mathrm{z}^{\mathrm{3}} }\:=\:\mathrm{18}\:\sqrt[{\mathrm{3}}]{\mathrm{3z}\:+\:\mathrm{2}} \\ $$ Commented by MJS_new last updated on 16/Sep/21 $$\mathrm{check}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of} \\…
Question Number 88752 by wiWiw last updated on 12/Apr/20 $$\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\alpha}\right)+\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\beta}\right)+\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\gamma}\right)\leqslant\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{prove}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{inequality}} \\ $$ Commented by TANMAY PANACEA. last updated on 12/Apr/20 Commented by TANMAY…
Question Number 154286 by EDWIN88 last updated on 16/Sep/21 $$\:{h}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{52}−\mathrm{47}{i}}\:+\sqrt[{\mathrm{3}}]{\mathrm{52}+\mathrm{47}{i}}\: \\ $$$$\:{find}\:{h}^{\mathrm{2}} . \\ $$ Commented by MJS_new last updated on 16/Sep/21 $${r}^{\mathrm{1}/\mathrm{3}} \mathrm{e}^{\mathrm{i}\theta/\mathrm{3}} +{r}^{\mathrm{1}/\mathrm{3}}…
Question Number 23208 by Joel577 last updated on 27/Oct/17 $$\mathrm{Is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{find}\:\mathrm{how}\:\mathrm{many}\:\mathrm{real}\:\mathrm{roots}\: \\ $$$$\mathrm{exist}\:\mathrm{in}\:\mathrm{the}\:\mathrm{equation} \\ $$$${x}^{\mathrm{4}} \:+\:\mid{x}\mid\:=\:\mathrm{3} \\ $$$$\mathrm{without}\:\mathrm{find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{x}? \\ $$ Answered by mrW1 last updated on…
Question Number 154275 by mathdanisur last updated on 16/Sep/21 Commented by benhamimed last updated on 16/Sep/21 $$=\Pi\frac{\left(\mathrm{1}+{n}^{\mathrm{2}} \right)^{\mathrm{2}} }{\left({n}^{\mathrm{2}} +\mathrm{2}\right)^{\mathrm{2}} −\left(\mathrm{2}{n}\right)^{\mathrm{2}} }=\Pi\frac{\left(\mathrm{1}+{n}^{\mathrm{2}} \right)^{\mathrm{2}} }{\left({n}^{\mathrm{2}} −\mathrm{2}{n}+\mathrm{2}\right)\left({n}^{\mathrm{2}}…
Question Number 154273 by amin96 last updated on 16/Sep/21 Answered by MJS_new last updated on 16/Sep/21 $${x}\approx\mathrm{1}.\mathrm{05582160} \\ $$$${y}\approx.\mathrm{583496355} \\ $$ Commented by amin96 last…
Question Number 154274 by mathdanisur last updated on 16/Sep/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{x}^{\mathrm{2}} \centerdot\mathrm{2}^{\boldsymbol{\mathrm{x}}} \left(\mathrm{x}^{\mathrm{4}} \centerdot\mathrm{4}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{3}\centerdot\mathrm{15}^{\boldsymbol{\mathrm{x}}} \right)\:=\:\mathrm{125}^{\boldsymbol{\mathrm{x}}} \:-\:\mathrm{27}^{\boldsymbol{\mathrm{x}}} \\ $$ Commented by MJS_new last updated…
Question Number 154267 by mathdanisur last updated on 16/Sep/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\mathrm{and}\:\mathrm{xy}+\mathrm{yz}+\mathrm{zx}=\mathrm{3xyz}\:\:\mathrm{then}: \\ $$$$\left(\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{1}}{\mathrm{x}+\mathrm{y}}\right)\left(\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{1}}{\mathrm{2x}+\mathrm{y}+\mathrm{z}}\right)\:\leqslant\:\frac{\mathrm{9}}{\mathrm{8}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com