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
Question Number 154262 by mathlove last updated on 16/Sep/21 Answered by som(math1967) last updated on 16/Sep/21 $${lntan}\left(\frac{\pi}{\mathrm{180}}\right)+{lntan}\left(\frac{\mathrm{2}\pi}{\mathrm{180}}\right)+…{lntan}\left(\frac{\mathrm{89}\pi}{\mathrm{180}}\right) \\ $$$${lntan}\mathrm{1}°+{lntan}\mathrm{2}°+…{lntan}\mathrm{89}°\bigstar \\ $$$${lntan}\mathrm{1}×{tan}\mathrm{2}×…{tan}\mathrm{89} \\ $$$${lntan}\mathrm{1}×{cot}\left(\mathrm{90}−\mathrm{89}\right)×{tan}\mathrm{2}×{cot}\left(\mathrm{90}−\mathrm{88}\right)…×{tan}\mathrm{45} \\ $$$${lntan}\mathrm{1}×{cot}\mathrm{1}×{tan}\mathrm{2}×{cot}\mathrm{2}×…×\mathrm{1}…
Question Number 154258 by liberty last updated on 16/Sep/21 Answered by som(math1967) last updated on 16/Sep/21 $$\frac{{a}}{{b}+{c}}\:+\mathrm{1}+\frac{{b}}{{c}+{a}}+\mathrm{1}+\frac{{c}}{{a}+{b}}+\mathrm{1}=\mathrm{76}+\mathrm{3} \\ $$$$\:{or}\:\frac{{a}+{b}+{c}}{{b}+{c}}\:+\frac{{a}+{b}+{c}}{{c}+{a}}\:+\frac{{a}+{b}+{c}}{{a}+{b}}=\mathrm{79} \\ $$$${or}.\:\left({a}+{b}+{c}\right)\left(\frac{\mathrm{1}}{{b}+{c}}+\frac{\mathrm{1}}{{c}+{a}}+\frac{\mathrm{1}}{{a}+{b}}\right)=\mathrm{79} \\ $$$$\therefore\left(\frac{\mathrm{1}}{{a}+{b}}\:+\frac{\mathrm{1}}{{b}+{c}}+\frac{\mathrm{1}}{{c}+{a}}\right)=\frac{\mathrm{79}}{\mathrm{1580}}=\frac{\mathrm{1}}{\mathrm{20}}\bigstar \\ $$$$\bigstar{a}+{b}+{c}=\mathrm{1580}…