Question Number 144549 by mathdanisur last updated on 26/Jun/21 Answered by qaz last updated on 27/Jun/21 $$\mathrm{if}\:\mathrm{y}=\mathrm{z}=\mathrm{t}=\mathrm{2},\mathrm{x}=\mathrm{3},\mathrm{this}\:\mathrm{inequality}\:\mathrm{does}\:\mathrm{not}\:\mathrm{hold}…. \\ $$ Terms of Service Privacy Policy Contact:…
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Question Number 144537 by loveineq last updated on 26/Jun/21 $$\mathrm{Let}\:{a},{b}>\mathrm{0}\:\mathrm{and}\:{a}+{b}\:=\:\mathrm{2}.\:\mathrm{Prove}\:\mathrm{that}\:\:\:\:\:\:\:\:\:\: \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{3}} +{b}^{\mathrm{3}} }{\mathrm{2}}−\mathrm{2}\left(\mathrm{1}−{ab}\right)\:\geqslant\:\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }{\mathrm{2}}−\mathrm{2}\left(\mathrm{1}−{ab}\right)\:\leqslant\:\mathrm{1} \\ $$ Answered by mnjuly1970 last updated…
Question Number 13438 by Nayon last updated on 20/May/17 $$\mathrm{7}{x}^{\mathrm{5}} −\mathrm{4}{x}^{\mathrm{4}} +\mathrm{9}{x}^{\mathrm{3}} +\mathrm{12}{x}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{9}=\mathrm{0} \\ $$$${How}\:{many}\:{roots}\:{of}\:{this}\:{equation} \\ $$$${are}\:{Negative}? \\ $$$$ \\ $$ Answered by mrW1…
Question Number 78948 by TawaTawa last updated on 21/Jan/20 $$\mathrm{Prove}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}\:\mathrm{that}. \\ $$$$\:\:\:\mathrm{n}^{\mathrm{4}} \:+\:\mathrm{4n}^{\mathrm{2}} \:+\:\mathrm{11}\:\:\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{16} \\ $$ Commented by john santu last updated on 21/Jan/20 $${let}\:{p}\left({n}\right)\:=\:{n}^{\mathrm{4}}…
Question Number 13412 by tawa tawa last updated on 19/May/17 $$\mathrm{e}^{−\mathrm{kN}} \:−\:\mathrm{kN}\:\:−\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{N} \\ $$ Answered by mrW1 last updated on 20/May/17 $${e}^{−{kN}} ={kN}+\mathrm{1}…
Question Number 144468 by mathdanisur last updated on 25/Jun/21 Commented by Rasheed.Sindhi last updated on 26/Jun/21 $${It}'{s}\:{sufficient}\:{to}\:{say}\:'{natural}\:{numbers}' \\ $$$${instead}\:{of}\:'{positive}\:{natural}\:{numbers}'. \\ $$ Terms of Service Privacy…
Question Number 144470 by mathdanisur last updated on 25/Jun/21 $${Solve}\:{for}\:{real}\:{positive}\:{numbers}\:{the} \\ $$$${equation}: \\ $$$$\boldsymbol{{z}}^{\boldsymbol{{log}}\left(\mathrm{3}\right)} \:+\:\boldsymbol{{z}}^{\boldsymbol{{log}}\left(\mathrm{4}\right)} \:+\:\boldsymbol{{z}}^{\boldsymbol{{log}}\left(\mathrm{5}\right)} \:=\:\boldsymbol{{z}}^{\boldsymbol{{log}}\left(\mathrm{6}\right)} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 78931 by mr W last updated on 21/Jan/20 $${if}\:{x}+\frac{\mathrm{1}}{{x}}={a} \\ $$$${find}\:{x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }=? \\ $$ Commented by mathmax by abdo last updated on…
Question Number 13395 by Tinkutara last updated on 19/May/17 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers}\:{n}\:\mathrm{for}\:\mathrm{which} \\ $$$${n}^{\mathrm{2}} \:+\:\mathrm{96}\:\mathrm{is}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$ Answered by ajfour last updated on 19/May/17 $$\left({n}+{m}\right)^{\mathrm{2}} ={n}^{\mathrm{2}} +\mathrm{96}…