Question Number 176948 by mathlove last updated on 28/Sep/22 Commented by mr W last updated on 28/Sep/22 $${what}\:{do}\:{mean}\:{with}\:\mathrm{9}!!!!\:{and}\:\mathrm{8}!!!!!? \\ $$$${can}\:{you}\:{tell}\:{a}\:{source}\:{where}\:{those} \\ $$$${notations}\:{are}\:{commonly}\:{defined}? \\ $$ Commented…
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Question Number 176898 by adhigenz last updated on 27/Sep/22 Answered by Rasheed.Sindhi last updated on 27/Sep/22 $$\alpha+\beta=−{m}\:,\:\alpha\beta={n} \\ $$$$\alpha^{\mathrm{3}} +\beta^{\mathrm{3}} =\left(\alpha+\beta\right)\left(\:\left(\alpha+\beta\right)^{\mathrm{2}} −\mathrm{3}\alpha\beta\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=−{m}\left(\:\left(−{m}\right)^{\mathrm{2}} −\mathrm{3}\left({n}\right)\:\right)…
Question Number 176893 by infinityaction last updated on 27/Sep/22 $$\:\:\:\:\left[\mathrm{4}\left({x}^{\mathrm{2}} +\mathrm{2}\right)\:+\frac{\mathrm{9}}{\left({x}^{\mathrm{2}} +\mathrm{2}\right)}\right]_{\mathrm{min}} \\ $$ Answered by mr W last updated on 27/Sep/22 $${t}={x}^{\mathrm{2}} +\mathrm{2}\geqslant\mathrm{2} \\…
Question Number 176894 by infinityaction last updated on 27/Sep/22 Answered by BaliramKumar last updated on 27/Sep/22 $$\Rightarrow\:\frac{\left(\frac{\mathrm{28}×\mathrm{29}×\mathrm{30}×\mathrm{31}×……..×\mathrm{76}}{\mathrm{49}!}\right)}{\left(\frac{\mathrm{50}×\mathrm{51}×\mathrm{52}×\mathrm{53}×………×\mathrm{76}}{\mathrm{27}!}\right)} \\ $$$$\Rightarrow\:\frac{\mathrm{27}!\left(\mathrm{28}×\mathrm{29}×\mathrm{30}×\mathrm{31}×……..×\mathrm{76}\right)}{\mathrm{49}!\left(\mathrm{50}×\mathrm{51}×\mathrm{52}×\mathrm{53}×…….×\mathrm{76}\right)}\: \\ $$$$\Rightarrow\: \\ $$$$\Rightarrow\:\frac{\mathrm{76}!}{\mathrm{76}!}\:=\:\begin{array}{|c|}{\mathrm{1}}\\\hline\end{array} \\ $$…
Question Number 176891 by Shrinava last updated on 27/Sep/22 Answered by mr W last updated on 27/Sep/22 $$\mathrm{sin}\:{x}\:\mathrm{cos}\:\mathrm{3}{x}\:\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{2}\:\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}\:\left(\frac{\mathrm{cos}\:{x}}{\mathrm{2}}+\frac{\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}}{\mathrm{2}}\right)\left(\frac{\mathrm{cos}\:{x}}{\mathrm{2}}−\frac{\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}}{\mathrm{2}}\right) \\ $$$$\mathrm{cos}\:\mathrm{3}{x}\:=\:\mathrm{cos}\:{x}\:\left(\mathrm{cos}^{\mathrm{2}} \:{x}−\mathrm{3}\:\mathrm{sin}^{\mathrm{2}} \:{x}\right) \\ $$$$\mathrm{4}\:\mathrm{cos}^{\mathrm{2}} \:{x}−\mathrm{3}\:=\:\mathrm{cos}^{\mathrm{2}}…
Question Number 111344 by Study last updated on 03/Sep/20 $$\sqrt{\mathrm{3}}!=? \\ $$ Commented by Dwaipayan Shikari last updated on 03/Sep/20 $$\mathrm{1}.\mathrm{585000}… \\ $$ Commented by…
Question Number 111343 by Study last updated on 03/Sep/20 $${i}!=? \\ $$ Commented by Dwaipayan Shikari last updated on 03/Sep/20 $$\Gamma\left(\mathrm{1}+{i}\right)=\mathrm{0}.\mathrm{4980}−\mathrm{0}.\mathrm{1549}{i} \\ $$ Terms of…
Question Number 176846 by Ar Brandon last updated on 27/Sep/22 $${m}\in\mathbb{Z} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{leading}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{the}\:\mathrm{polynomial} \\ $$$$\mathrm{P}\left({x}\right)=\mathrm{4}{x}^{\frac{\mathrm{13}}{{m}−\mathrm{5}}} −\mathrm{6}{x}^{\mathrm{25}−\mathrm{2}{m}} +\mathrm{4}{x}^{\mathrm{13}} +\mathrm{5}{x}^{\mathrm{10}} −\mathrm{4}\:? \\ $$ Answered by mr W…
Question Number 176773 by Ar Brandon last updated on 26/Sep/22 $$\mathrm{Let}\:{a},\:{b},\:{c}\:>\mathrm{0}.\:\mathrm{If}\: \\ $$$$\frac{{a}−{b}}{{b}}>\mathrm{7},\:\frac{{b}+{c}}{{c}}<\mathrm{8},\: \\ $$$$\mathrm{Find}\:\mathrm{min}\left({a}+{b}+{c}\right)\: \\ $$ Commented by Ar Brandon last updated on 26/Sep/22…