Question Number 155653 by mathdanisur last updated on 03/Oct/21 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}\geqslant\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{1}\:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{18}\:\Sigma\:\mathrm{ab}\:+\:\mathrm{45}\:\Sigma\:\mathrm{a}^{\mathrm{2}} \mathrm{b}\:\leqslant\:\mathrm{11} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 24576 by math solver last updated on 21/Nov/17 Commented by math solver last updated on 21/Nov/17 $$\mathrm{sum}\:\mathrm{of}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{is}\:? \\ $$ Answered by mrW1 last…
Question Number 90103 by A8;15: last updated on 21/Apr/20 Commented by john santu last updated on 21/Apr/20 $${translate} \\ $$ Terms of Service Privacy Policy…
Question Number 24565 by ajfour last updated on 21/Nov/17 $$\:\:\boldsymbol{{y}}=\boldsymbol{{ax}}^{\mathrm{3}} +\boldsymbol{{bx}}^{\mathrm{2}} +\boldsymbol{{cx}}+\boldsymbol{{d}}\:,\:{then} \\ $$$${prove}\:{that}\:{the}\:{equation}\:{y}=\mathrm{0} \\ $$$${has}\:{only}\:{one}\:{real}\:{root}\:{if} \\ $$$$\:\boldsymbol{{a}}\left[\left(\mathrm{9}\boldsymbol{{ad}}−\boldsymbol{{bc}}\right)^{\mathrm{2}} −\mathrm{4}\left(\boldsymbol{{b}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{{ac}}\right)\left(\boldsymbol{{c}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{{bd}}\right)\right] \\ $$$$\:\:\:\:>\:\mathrm{0}\:\:\:\:\:{provided}\:\:\:\boldsymbol{{b}}^{\mathrm{2}} \:>\:\mathrm{3}\boldsymbol{{ac}}\:. \\…
Question Number 90097 by jagoll last updated on 21/Apr/20 $$\left(\sqrt{\mathrm{3}+\sqrt{\mathrm{8}}}\right)^{\mathrm{x}} \:+\left(\sqrt{\mathrm{3}−\sqrt{\mathrm{8}}}\right)^{\mathrm{x}} \:=\:\mathrm{6} \\ $$ Commented by john santu last updated on 21/Apr/20 $$\left(\mathrm{3}+\sqrt{\mathrm{8}}\right)\left(\mathrm{3}−\sqrt{\mathrm{8}}\right)=\mathrm{1} \\ $$$$\mathrm{3}−\sqrt{\mathrm{8}}\:=\:\frac{\mathrm{1}}{\mathrm{3}+\sqrt{\mathrm{8}}}\:…
Question Number 90092 by jagoll last updated on 21/Apr/20 $$\mathrm{G}\left(\sqrt{\mathrm{x}+\mathrm{5}}\right)\:=\:\mathrm{x} \\ $$$$\mathrm{G}\left(\mathrm{x}^{\mathrm{2}} \right)\:=\:\mathrm{x}^{\mathrm{a}} −\mathrm{b} \\ $$$$\mathrm{find}\:\mathrm{a}+\mathrm{b}\: \\ $$ Commented by john santu last updated on…
Question Number 155621 by mathdanisur last updated on 02/Oct/21 Answered by ghimisi last updated on 03/Oct/21 $$\frac{{a}+{b}+{c}}{\mathrm{6}}=\mathrm{1}\Rightarrow \\ $$$$\left(\frac{{a}+{d}}{{a}}\right)^{\frac{{a}}{\mathrm{6}}} \left(\frac{{b}+{e}}{{b}}\right)^{\frac{{b}}{\mathrm{6}}} \left(\frac{{c}+{f}}{{c}}\right)^{\frac{{c}}{\mathrm{6}}} \leqslant\frac{{a}}{\mathrm{6}}\centerdot\frac{{a}+{d}}{{a}}+\frac{{b}}{\mathrm{6}}\centerdot\frac{{b}+{e}}{{b}}+\frac{{c}}{\mathrm{6}}\centerdot\frac{{c}+{f}}{{c}}=\mathrm{2}\Rightarrow \\ $$$$\left(\frac{{a}+{d}}{{a}}\right)^{{a}} \left(\frac{{b}+{c}}{{b}}\right)^{{b}}…
Question Number 155620 by mathdanisur last updated on 02/Oct/21 $$\mathrm{Find}:\:\:\:\boldsymbol{\Omega}\:=\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\underset{\boldsymbol{\mathrm{x}}-\mathrm{1}} {\overset{\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} -\boldsymbol{\mathrm{e}}} {\int}}\mathrm{cos}\left(\mathrm{t}^{\mathrm{5}} \right)\mathrm{dt}}{\mathrm{3}^{\boldsymbol{\mathrm{x}}} \:-\:\mathrm{3}}\:=\:? \\ $$ Answered by mindispower last updated on 04/Oct/21…
Question Number 90086 by I want to learn more last updated on 21/Apr/20 Commented by I want to learn more last updated on 21/Apr/20 $$\mathrm{Ohh},\:\:\mathrm{i}\:\mathrm{grab}…
Question Number 24548 by Physics lover last updated on 20/Nov/17 $${prove}\:{that}\: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{{r}} {\sum}}\left\{{n}\left({n}−\frac{{r}}{\mathrm{2}}\right)^{\mathrm{2}} \right\}=\:{r}\centerdot\underset{{n}=\mathrm{1}} {\overset{{r}/\mathrm{2}} {\sum}}{n}^{\mathrm{2}} \\ $$$$\:{where}\:\:\:{r}\:=\:\mathrm{2}{k}\:;\:{k}\:\in\:\mathbb{N} \\ $$ Answered by jota…