Question Number 159119 by HongKing last updated on 13/Nov/21 $$\mathrm{Assume}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{12} \\ $$$$\mathrm{Prove}\:\mathrm{that}:\:\:\underset{\boldsymbol{\mathrm{cycl}}} {\sum}\:\frac{\frac{\mathrm{x}}{\mathrm{y}}\:+\:\mathrm{1}\:+\:\frac{\mathrm{y}}{\mathrm{x}}}{\frac{\mathrm{1}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{y}}}\:\leqslant\:\mathrm{9} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 159097 by depressiveshrek last updated on 12/Nov/21 $${f}\left({x}\right)={log}_{\mathrm{2}\:} ^{{x}} \left(\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\:\sqrt{{x}+\mathrm{1}}}\right)+\mid{x}\mid^{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 159092 by HongKing last updated on 12/Nov/21 Answered by Rasheed.Sindhi last updated on 13/Nov/21 $$\left({i}\right){a}\left({a}−{b}\right)=\mathrm{2018} \\ $$$$\begin{cases}{{a}=\mathrm{1}\:\wedge\:{a}−{b}=\mathrm{2018}\Rightarrow{b}=−\mathrm{2017}<\mathrm{0}}\\{{a}=\mathrm{2018}\:\wedge\:{a}−{b}=\mathrm{1}\Rightarrow{b}=\mathrm{2017}}\\{{a}=\mathrm{2}\:\wedge\:{a}−{b}=\mathrm{1009}\Rightarrow{b}=−\mathrm{1007}<\mathrm{0}}\\{{a}=\mathrm{1009}\:\wedge\:{a}−{b}=\mathrm{2}\Rightarrow{b}=\mathrm{1007}}\end{cases} \\ $$$${Possible}\:{solutions}\:\left({a},{b}\right)=\left(\mathrm{2018},\mathrm{2017}\right), \\ $$$$\left(\mathrm{1009},\mathrm{1007}\right) \\ $$$$\left({ii}\right)\:{bc}+{ac}−{b}^{\mathrm{2}}…
Question Number 159086 by HongKing last updated on 12/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 159072 by quvonnn last updated on 12/Nov/21 Commented by quvonnn last updated on 12/Nov/21 $$??? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 159066 by amin96 last updated on 12/Nov/21 $$\mathrm{16}/\mathrm{4}\left(\mathrm{2}+\mathrm{2}\right)=? \\ $$ Commented by Rasheed.Sindhi last updated on 12/Nov/21 $$\mathrm{2}\:\mathrm{Conventions}: \\ $$$$\left(\mathrm{i}\right)\mathrm{implied}\:\mathrm{multiplication}\:\mathrm{has}\:\mathrm{priority} \\ $$$$\:\:\:\:\:\:\:\mathrm{over}\:\mathrm{division}: \\…
Question Number 27996 by JI Siam last updated on 18/Jan/18 $$\mathrm{p},\mathrm{q}\:\mathrm{are}\:\mathrm{two}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{and}\: \\ $$$$\:\frac{\mathrm{p}^{\mathrm{6}} +\mathrm{2p}^{\mathrm{4}} +\mathrm{4p}^{\mathrm{2}} }{\mathrm{p}^{\mathrm{9}} −\mathrm{8p}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{4q}}=\frac{\mathrm{5}}{\mathrm{6q}}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{p}+\mathrm{q} \\ $$ Answered…
Question Number 159057 by HongKing last updated on 12/Nov/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{positive}\:\mathrm{integers}: \\ $$$$\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{9b}^{\mathrm{2}} \:+\:\mathrm{9c}^{\mathrm{2}} \:=\:\mathrm{2017} \\ $$$$\mathrm{where}\:\:\mathrm{a}\:\geqslant\:\mathrm{b}\:\geqslant\:\mathrm{c} \\ $$$$ \\ $$ Commented by Rasheed.Sindhi last…
Question Number 159049 by mnjuly1970 last updated on 12/Nov/21 $$ \\ $$$$\:\:\:\:\:\:{solve}\:{the}\:{following}\:{equation}: \\ $$$$\: \\ $$$${sin}^{\:\mathrm{6}} \left({x}\right)\:+{cos}^{\:\mathrm{6}} \left({x}\right)+{sin}^{\mathrm{4}} \left({x}\right)+{cos}^{\:\mathrm{4}} \left({x}\right)=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$ \\ $$ Answered…
Question Number 27983 by JI Siam last updated on 18/Jan/18 $$\left.\mathrm{1}\right)\:\mathrm{find}\:\mathrm{two}\:\:\mathrm{factors}\:\mathrm{of}\:\mathrm{1000001}\:\mathrm{other}\:\mathrm{than}\:\mathrm{1}\:\mathrm{and}\:\mathrm{1000001} \\ $$$$\left.\mathrm{2}\right)\left(\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{5}\right)^{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{24}\right)} =\mathrm{1}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\:\mathrm{of}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{solutions}? \\ $$ Answered by mrW2 last updated on 18/Jan/18…