Question Number 17595 by virus last updated on 08/Jul/17 $${Let}\:{a},{b},{c}\:{be}\:{the}\:{posetive}\:{integer}\:{such}\:{that}\: \\ $$$${b}/{a}\:{is}\:{an}\:{also}\:{integer}\:{if}\:{a},{b},{c}\:{are}\:{in}\:{GP}\:{and}\: \\ $$$${AM}\:{of}\:{a},{b},{c}\:{is}\left({b}+\mathrm{2}\right)\:{then}\:{find}\:{the}\:{value}\:{of} \\ $$$$\left({a}^{\mathrm{2}} +{a}−\mathrm{14}\right)/\left({a}+\mathrm{1}\right) \\ $$ Commented by virus last updated on…
Question Number 148559 by Jonathanwaweh last updated on 29/Jul/21 Answered by Kamel last updated on 29/Jul/21 $${a}=\mathrm{3}{k}+{r},{b}=\mathrm{3}{k}'+{r}'\:\mathrm{0}\leqslant{r}<\mathrm{3},\:\mathrm{0}\leqslant{r}'<\mathrm{3}. \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{3}{c}=\mathrm{9}\left({k}^{\mathrm{2}} +{k}'^{\mathrm{2}} \right)+\mathrm{6}\left({kr}+{k}'{r}'\right)+{r}^{\mathrm{2}} +{r}'^{\mathrm{2}} \\…
Question Number 82995 by M±th+et£s last updated on 26/Feb/20 Commented by mr W last updated on 26/Feb/20 $${a}_{\mathrm{1000}} =\frac{\mathrm{1}}{\mathrm{499501}}\:? \\ $$ Answered by mind is…
Question Number 148483 by puissant last updated on 28/Jul/21 $$\mathrm{Soit}\:\mathrm{f}\:\mathrm{une}\:\mathrm{fonction}\:\mathrm{continu}\:\mathrm{sur}\:\mathbb{R} \\ $$$$\mathrm{et}\:\mathrm{non}\:\mathrm{identiquement}\:\mathrm{nulle}, \\ $$$$\forall\:\mathrm{x},\mathrm{x}'\in\mathbb{R},\:\mathrm{f}\left(\mathrm{x}−\mathrm{x}'\right)+\mathrm{f}\left(\mathrm{x}+\mathrm{x}'\right)=\mathrm{2f}\left(\mathrm{x}\right)\mathrm{f}\left(\mathrm{x}'\right) \\ $$$$\mathrm{montrer}\:\mathrm{que}: \\ $$$$\mathrm{f}\left(\mathrm{0}\right)=\mathrm{1}\:\mathrm{et}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(−\mathrm{x}\right).. \\ $$ Answered by Olaf_Thorendsen last updated…
Question Number 17401 by ajfour last updated on 05/Jul/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{4}-\mathrm{digit}\:\mathrm{greatest} \\ $$$$\mathrm{number}\:\mathrm{and}\:\mathrm{the}\:\mathrm{5}-\mathrm{digit}\:\mathrm{smallest} \\ $$$$\mathrm{number},\:\mathrm{each}\:\mathrm{number}\:\mathrm{having}\:\mathrm{three} \\ $$$$\mathrm{different}\:\mathrm{digits}. \\ $$ Commented by RasheedSoomro last updated on 05/Jul/17…
Question Number 148398 by puissant last updated on 27/Jul/21 Answered by Olaf_Thorendsen last updated on 27/Jul/21 $$\mathrm{1}.\:\mathrm{C}_{\mathrm{1}} \:=\:\mathrm{7}{l}\:\mathrm{et}\:\mathrm{C}_{\mathrm{2}} \:=\:\mathrm{4}{l} \\ $$$$ \\ $$$$\bullet\:\mathrm{Etape}\:\mathrm{1}. \\ $$$$\mathrm{Je}\:\mathrm{remplis}\:\mathrm{C}_{\mathrm{1}}…
Question Number 82839 by M±th+et£s last updated on 24/Feb/20 $${if}\:{the}\:{first}\:{and}\:{fifth}\:{terms}\:{of}\:{arithmetic} \\ $$$${peogression}\:{are}\:{equal}\:{and}\:{the}\:{seventh} \\ $$$${and}\:{fourtenth}\:{terms}\:{of}\:{another}\:{arithmetic}\:{are} \\ $$$${equal}\:{then}\:{show}\:{that}\:{the}\:{first}\:{term}\:{from} \\ $$$${the}\:{first}\:{arithmetic}\:{is}\:{equal}\:{the}\:{tenth} \\ $$$${from}\:{the}\:{second}\:{one} \\ $$$${and}\:{so}\:{sorry}\:{because}\:{my}\:{english}\:{is} \\ $$$${not}\:{so}\:{good} \\…
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Question Number 17280 by tawa tawa last updated on 03/Jul/17 $$\mathrm{prove}\:\mathrm{that}:\:\:\mathrm{cosh}\left(\mathrm{2x}\right)\:=\:\mathrm{2cosh}^{\mathrm{2}} \left(\mathrm{x}\right)\:−\:\mathrm{1} \\ $$ Commented by mrW1 last updated on 03/Jul/17 $$\mathrm{cosh}\:\left(\mathrm{2x}\right)=\frac{\mathrm{e}^{\mathrm{2x}} +\mathrm{e}^{−\mathrm{2x}} }{\mathrm{2}} \\…
Question Number 148334 by Sravanth last updated on 27/Jul/21 Answered by Rasheed.Sindhi last updated on 27/Jul/21 $$\mathrm{3}^{\mathrm{6}} ×\left(\mathrm{2}^{−\mathrm{2}} ×\mathrm{3}^{\mathrm{5}×−\mathrm{2}} \right)×\left(\mathrm{2}×\mathrm{3}^{\mathrm{2}} \right)^{\mathrm{2}} \\ $$$$\mathrm{3}^{\mathrm{6}} ×\mathrm{2}^{−\mathrm{2}} ×\mathrm{3}^{−\mathrm{10}}…