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Question Number 32767 by Rasheed.Sindhi last updated on 01/Apr/18 $$\mathrm{For}\:{a},{b},{c}\geqslant\mathrm{0}\:\mathrm{if}\:{a}+{b}+{c}={n},\:\mathrm{determine} \\ $$$$\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum}\:\mathrm{values}\:\mathrm{of} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{ab}−{bc}−{ca}. \\ $$ Commented by Rasheed.Sindhi last updated on…
Question Number 32768 by Rasheed.Sindhi last updated on 01/Apr/18 $$\mathrm{Prove}\:\mathrm{that}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} \geqslant{ab}+{bc}+{ca} \\ $$$$\forall\:{a},{b},{c}\in\mathbb{R} \\ $$ Answered by mrW2 last updated on 02/Apr/18 $${a}^{\mathrm{2}}…
Question Number 163833 by mathlove last updated on 11/Jan/22 Commented by mr W last updated on 11/Jan/22 $${x}=\overset{\sim} {\boldsymbol{\mathcal{W}}}\left(\mathrm{36}\right)\approx\mathrm{2}.\mathrm{107036463957} \\ $$ Commented by Tawa11 last…
Question Number 98293 by I want to learn more last updated on 12/Jun/20 Answered by mr W last updated on 12/Jun/20 $${see}\:{Q}\mathrm{97675} \\ $$$${x}+{y}+{z}=\mathrm{0} \\…
Question Number 98280 by I want to learn more last updated on 12/Jun/20 $$\boldsymbol{\mathrm{Let}}\:\:\left\{\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \right\}\:\:\boldsymbol{\mathrm{be}}\:\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{sequence}}\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\:\:\boldsymbol{\mathrm{a}}_{\mathrm{1}} \:=\:\:\mathrm{2}, \\ $$$$\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}\:\:+\:\:\mathrm{1}} \:\:=\:\:\frac{\mathrm{3}\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \:+\:\:\mathrm{4}}{\mathrm{2}\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \:\:+\:\:\mathrm{3}},\:\:\:\:\:\boldsymbol{\mathrm{n}}\:\geqslant\:\mathrm{1},\:\:\:\:\:\boldsymbol{\mathrm{find}}\:\:\:\:\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \\ $$ Answered by…
Question Number 163812 by mathlove last updated on 11/Jan/22 Answered by cortano1 last updated on 11/Jan/22 $$\:{p}\left({x}\right)=\:{x}^{\mathrm{3}} +\mathrm{1} \\ $$$$\:{p}\left(\mathrm{4}\right)=\:\mathrm{65} \\ $$ Commented by mathlove…
Question Number 98268 by mr W last updated on 16/Jun/20 $${let}\:{p}\left({x}\right)\:{be}\:{a}\:{polynomial}\:{function}\:{of} \\ $$$$\left({n}−\mathrm{1}\right)^{{th}} \:{degree}\:{and} \\ $$$${p}\left({k}\right)={k}\:{for}\:{k}=\mathrm{1},\mathrm{2},\mathrm{3},…,{n} \\ $$$${find}\:{p}\left(\mathrm{0}\right)\:{and}\:{p}\left({n}+\mathrm{1}\right). \\ $$$${example}:\:{n}=\mathrm{10} \\ $$ Commented by MJS…
Question Number 98267 by M±th+et+s last updated on 12/Jun/20 $$\forall\:{a},{b}>\mathrm{0}\:,\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{1} \\ $$$${prove}\:{that} \\ $$$$\left(\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}\right)\left(\frac{{b}}{{a}^{\mathrm{2}} +\mathrm{1}}+\frac{{a}}{{b}^{\mathrm{2}} +\mathrm{1}}\right)\geqslant\frac{\mathrm{8}}{\mathrm{3}} \\ $$ Answered by maths mind last…
Question Number 163782 by bekzodjumayev last updated on 10/Jan/22 Commented by bekzodjumayev last updated on 10/Jan/22 $${Please}\:{help} \\ $$ Answered by Ar Brandon last updated…