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Question Number 187373 by Shrinava last updated on 16/Feb/23 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{natural}\:\mathrm{numbers}: \\ $$$$\mathrm{31}\:+\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\left(\begin{pmatrix}{\mathrm{n}}\\{\mathrm{k}}\end{pmatrix}\:\:\centerdot\:\underset{\boldsymbol{\mathrm{m}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{m}^{\boldsymbol{\mathrm{n}}−\boldsymbol{\mathrm{k}}} \right)\:=\:\mathrm{31}^{\mathrm{30}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 187357 by cortano12 last updated on 16/Feb/23 Answered by Humble last updated on 16/Feb/23 $$\mathrm{3}\sqrt{\mathrm{5}}\sqrt{\mathrm{2}{x}+\mathrm{3}}\:+\mathrm{2}\sqrt{\mathrm{5}}\sqrt{\mathrm{3}{x}+\mathrm{2}}\:=\:\sqrt{\mathrm{3}{x}+\mathrm{2}}\sqrt{\mathrm{2}{x}+\mathrm{3}} \\ $$$$ \\ $$$$\mathrm{21600}{x}^{\mathrm{2}} +\mathrm{46800}{x}+\mathrm{21600}=\mathrm{36}{x}^{\mathrm{4}} −\mathrm{1644}{x}^{\mathrm{3}} +\mathrm{16741}{x}^{\mathrm{2}} +\mathrm{46306}{x}+\mathrm{28561}…
Question Number 56264 by ajfour last updated on 13/Mar/19 $$\left({x}_{{C}} −{h}\right)^{\mathrm{2}} +\mathrm{3}\left(\frac{{s}}{\mathrm{2}}−{x}_{{C}} \right)^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \\ $$$$\:\left({x}_{{A}} −{h}\right)^{\mathrm{2}} +\mathrm{3}\left(\frac{{s}}{\mathrm{2}}+{x}_{{A}} \right)^{\mathrm{2}} =\:{c}^{\mathrm{2}} \\ $$$$\:\:\left({x}_{{C}} −{x}_{{A}} \right)^{\mathrm{2}} \:=\:{b}^{\mathrm{2}}…
Question Number 187302 by anurup last updated on 17/Feb/23 $${f}\left(\mathrm{4}\right)=\mathrm{44},\:{f}\left({m}\right)=\mathrm{52},{f}\left({l}\right)=−\mathrm{33} \\ $$$${l},{m}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{such}\:\mathrm{that}\:\mathrm{4}<{m}<{l} \\ $$$$\mathrm{and}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{with}\:\mathrm{integer}\:\mathrm{coefficients}. \\ $$$$\mathrm{Find}\:{l}+{m}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 187295 by Michaelfaraday last updated on 15/Feb/23 $${solve}: \\ $$$$\left(\sqrt{\left.\mathrm{4}+\sqrt{\mathrm{4}}\right)\:^{{x}} }\:+\left[\sqrt{\mathrm{4}−\sqrt{\left.\mathrm{4}\right]^{{x}} }}\:=\mathrm{4}^{{x}} \right.\right. \\ $$ Commented by MJS_new last updated on 15/Feb/23 $$\mathrm{not}\:\mathrm{clear}…
Question Number 187294 by Michaelfaraday last updated on 15/Feb/23 $${solve}: \\ $$$$−\mathrm{1}−\left[{x}^{{x}} −\mathrm{5}{x}+\mathrm{6}\right]^{{x}} =\mathrm{1} \\ $$ Commented by MJS_new last updated on 15/Feb/23 $$\left[{t}\right]=\lfloor{t}\rfloor\:\mathrm{or}\:…? \\…
Question Number 187288 by mathlove last updated on 15/Feb/23 $${logx}+{x}!=\mathrm{2} \\ $$$${x}=? \\ $$ Answered by Frix last updated on 15/Feb/23 $${x}!\:\mathrm{is}\:\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{N}\:\Rightarrow\:\mathrm{no}\:\mathrm{solution} \\ $$$$\mathrm{If}\:\mathrm{you}\:\mathrm{mean} \\…
Question Number 121754 by bemath last updated on 11/Nov/20 Answered by liberty last updated on 11/Nov/20 $$\mathrm{let}\:\mathrm{y}\:=\:\left(\mathrm{2020}!\right)^{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{ln}\:\mathrm{y}\:=\:\mathrm{2}\left(\mathrm{ln}\:\mathrm{2020}+\mathrm{ln}\:\mathrm{2019}+\mathrm{ln}\:\mathrm{2018}+…+\mathrm{ln}\:\mathrm{1}\right) \\ $$$$\mathrm{let}\:\mathrm{x}\:=\:\mathrm{2020}^{\mathrm{2020}} \\ $$$$\Rightarrow\mathrm{ln}\:\mathrm{x}\:=\:\mathrm{2020}\:\mathrm{ln}\:\left(\mathrm{2020}\right)\: \\ $$$$…
Question Number 56192 by 121194 last updated on 11/Mar/19 $$\mathrm{find}\:{z}_{\mathrm{1}} ,{z}_{\mathrm{2}} \in\mathbb{C} \\ $$$$\frac{\mathrm{1}}{{z}_{\mathrm{1}} +{z}_{\mathrm{2}} }=\frac{\mathrm{1}}{{z}_{\mathrm{1}} }+\frac{\mathrm{1}}{{z}_{\mathrm{2}} } \\ $$ Answered by MJS last updated…