Question Number 158364 by HongKing last updated on 03/Nov/21 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\mathrm{a}^{\mathrm{2}\boldsymbol{\mathrm{a}}-\left(\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}\right)} \:\centerdot\:\mathrm{b}^{\mathrm{2}\boldsymbol{\mathrm{b}}-\left(\boldsymbol{\mathrm{c}}+\boldsymbol{\mathrm{a}}\right)} \:\centerdot\:\mathrm{c}^{\mathrm{2}\boldsymbol{\mathrm{c}}-\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}\right)} \:\geqslant\:\mathrm{1} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 158365 by HongKing last updated on 03/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92831 by unknown last updated on 09/May/20 Commented by unknown last updated on 09/May/20 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\left({p},{q},{r}\right)\:\mathrm{if}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{are}\:\mathrm{real}\:\mathrm{number} \\ $$ Commented by unknown last updated on…
Question Number 158363 by HongKing last updated on 03/Nov/21 $$\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0} \\ $$$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \:+\:\mathrm{3}\centerdot\left(\sqrt[{\mathrm{3}}]{\mathrm{x}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{y}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{z}}\right)\:=\:\mathrm{12}}\\{\mathrm{x}\centerdot\mathrm{y}\centerdot\mathrm{z}\:=\:\mathrm{1}}\end{cases} \\ $$$$ \\ $$ Answered by GuruBelakangPadang last…
Question Number 158366 by HongKing last updated on 03/Nov/21 Answered by MathsFan last updated on 03/Nov/21 $$\frac{\mathrm{lne}}{\mathrm{lnx}\bullet\mathrm{lnx}}+\frac{\mathrm{lne}}{\left(\mathrm{lne}−\mathrm{lnx}\right)\left(\mathrm{lne}−\mathrm{lnx}\right)}=\mathrm{8} \\ $$$$\mathrm{say}\:\:\mathrm{a}=\mathrm{lnx} \\ $$$$\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{1}−\mathrm{2a}+\mathrm{a}^{\mathrm{2}} }=\mathrm{8} \\ $$$$\:\mathrm{2a}^{\mathrm{2}}…
Question Number 92820 by prince 5 last updated on 13/May/20 $${a}\:{convergent}\:{geometric}\:{sequence}\:{with} \\ $$$${first}\:{term}\:{a}\:{is}\:{such}\:{that}\:{the}\:{sum}\:{of} \\ $$$${the}\:{terms}\:{after}\:{the}\:{n}^{{th}} \:{term}\:{is} \\ $$$${three}\:{times}\:{the}\:{n}^{{th}} \:{term},\:{find}\:{the} \\ $$$${common}\:{ratio}\:{and}\:{show}\:{that}\:{its}\: \\ $$$${sum}\:{to}\:{infinity}\:{is}\:\mathrm{4}{a}. \\ $$…
Question Number 158331 by HongKing last updated on 02/Nov/21 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{n}}\:\left(\mathrm{n}\:+\:\mathrm{1}\right)}\:<\:\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92778 by unknown last updated on 09/May/20 Commented by prakash jain last updated on 09/May/20 $$\lfloor\mathrm{3}{x}\rfloor−\mathrm{2}−\left(\lfloor\mathrm{2}{x}\rfloor−\mathrm{1}\right)=\mathrm{2}{x}−\mathrm{6} \\ $$$$\lfloor\mathrm{3}{x}\rfloor−\lfloor\mathrm{2}{x}\rfloor=\mathrm{2}{x}−\mathrm{5}\: \\ $$$$\mathrm{since}\:\mathrm{LHS}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}\:\mathrm{RHS} \\ $$$$\mathrm{must}\:\mathrm{be}\:\mathrm{integer} \\…
Question Number 158313 by mnjuly1970 last updated on 02/Nov/21 Answered by mr W last updated on 02/Nov/21 $$\alpha,\beta,\gamma\:{are}\:{angles}\:{of}\:{a}\:{triangle}. \\ $$$${F}=\frac{\mathrm{sin}\:\alpha\:\mathrm{cos}\:\alpha+\mathrm{sin}\:\beta\:\mathrm{cos}\:\beta+\mathrm{sin}\:\gamma\:\mathrm{cos}\:\gamma}{\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\gamma} \\ $$$${F}=\frac{\mathrm{sin}\:\mathrm{2}\alpha+\mathrm{sin}\:\mathrm{2}\beta+\mathrm{sin}\:\mathrm{2}\gamma}{\mathrm{2}\:\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\gamma} \\ $$$${F}=\frac{\mathrm{4}\:\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\gamma}{\mathrm{2}\:\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\gamma} \\…
Question Number 158303 by HongKing last updated on 02/Nov/21 $$\mathrm{x};\mathrm{y};\mathrm{z};\mathrm{t}>\mathrm{0} \\ $$$$\mathrm{solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\mathrm{8x}^{\mathrm{4}} \:+\:\mathrm{64y}^{\mathrm{4}} \:+\:\mathrm{216z}^{\mathrm{4}} \:+\:\mathrm{1728t}^{\mathrm{4}} \:=\:\mathrm{1}}\\{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:+\:\mathrm{t}\:=\:\mathrm{1}}\end{cases} \\ $$$$ \\ $$ Answered by mr…