Question Number 118193 by mathocean1 last updated on 15/Oct/20 $${Given}\:{A}={n}^{\mathrm{2}} −\mathrm{2}{n}+\mathrm{2}\:,\:{B}={n}^{\mathrm{2}} +\mathrm{2}{n}+\mathrm{2} \\ $$$${n}\:\in\:\mathbb{N}^{\ast} −\left\{\mathrm{1}\right\}. \\ $$$${Show}\:{that}\:\forall\:{divisor}\:{of}\:{A}\:{which}\:{divise} \\ $$$${n}\:{can}\:{also}\:{divise}\:\mathrm{2}. \\ $$$${Show}\:{that}\:{all}\:{common}\:{divisor}\:{of}\: \\ $$$${A}\:{and}\:{B}\:{can}\:{divise}\:\mathrm{4}{n}. \\ $$…
Question Number 118184 by mathocean1 last updated on 15/Oct/20 $${factorise}\:{x}^{\mathrm{4}} +\mathrm{4} \\ $$ Commented by bemath last updated on 16/Oct/20 $$\left({x}^{\mathrm{2}} \right)^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} \:=\:\left({x}^{\mathrm{2}} +\mathrm{2}\right)^{\mathrm{2}}…
Question Number 118180 by mathocean1 last updated on 15/Oct/20 $${show}\:{that}\:{if}\:{n}\:{is}\:{odd}\:,\:{n}\left({n}^{\mathrm{2}} +\mathrm{3}\right)\:{is}\:{even}. \\ $$ Answered by floor(10²Eta[1]) last updated on 15/Oct/20 $$\mathrm{if}\:\mathrm{n}\:\mathrm{is}\:\mathrm{odd}\Rightarrow\mathrm{n}=\mathrm{2k}+\mathrm{1},\:\mathrm{k}\in\mathbb{Z} \\ $$$$\left(\mathrm{2k}+\mathrm{1}\right)\left(\left(\mathrm{2k}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{3}\right) \\…
Question Number 118181 by mathocean1 last updated on 15/Oct/20 $${find}\:{all}\:{numbers}\:>\mathrm{1}\:{from}\:\mathbb{N}\:{which} \\ $$$${their}\:{cube}\:{are}\:<\mathrm{18360} \\ $$ Commented by mathocean1 last updated on 15/Oct/20 $${thanks} \\ $$ Answered…
Question Number 118172 by I want to learn more last updated on 15/Oct/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{rhombus}\:\mathrm{with}\:\mathrm{side}\:\:\mathrm{8}\:\mathrm{cm} \\ $$ Answered by MJS_new last updated on 15/Oct/20 $$\mathrm{more}\:\mathrm{information}\:\mathrm{needed} \\…
Question Number 183668 by mnjuly1970 last updated on 28/Dec/22 $$ \\ $$$$\:\:\:\:\:\:{x}\:,\:{y}\:,\:{z}\:\in\mathbb{R}: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\mathrm{If}\:\:\:\:\begin{cases}{\frac{\mathrm{1}}{{x}}\:+\frac{\mathrm{1}}{{y}+{z}}\:=\frac{\mathrm{1}}{\mathrm{2}}}\\{\frac{\mathrm{1}}{{y}}\:+\frac{\mathrm{1}}{{x}+{z}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}}\\{\frac{\mathrm{1}}{{z}_{\:} }\:+\frac{\mathrm{1}}{{x}+{y}}\:=\frac{\mathrm{1}}{\mathrm{4}}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\:\:\:{x}\:,\:{y}\:,\:{z}\:=? \\ $$$$ \\ $$ Commented by…
Question Number 183669 by mnjuly1970 last updated on 28/Dec/22 $$ \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:\frac{{x}}{\mathrm{1}\:+\:{x}\:+\:{x}^{\:\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:{min}_{\:{f}} \:=\:? \\ $$ Answered by manolex last updated on 28/Dec/22…
Question Number 183660 by mr W last updated on 28/Dec/22 $${what}\:{is}\:{larger}, \\ $$$$\mathrm{2022}^{\mathrm{2022}} \:{or}\:\mathrm{2021}^{\mathrm{2023}} \:? \\ $$ Answered by Ar Brandon last updated on 28/Dec/22…
Question Number 52573 by Necxx last updated on 09/Jan/19 $${Find}\:{the}\:{relation}\:{between}\:{p}\:{q}\:{and}\:{r} \\ $$$${if}\:{one}\:{of}\:{the}\:{root}\:{of}\:{the}\:{equation} \\ $$$${px}^{\mathrm{2}} +{qx}+{r}=\mathrm{0}\:{is}\:{double}\:{the}\:{other}. \\ $$ Answered by mr W last updated on 09/Jan/19…
Question Number 52572 by Necxx last updated on 09/Jan/19 $${In}\:{the}\:{equation}\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0}.{One} \\ $$$${root}\:{is}\:{the}\:{square}\:{of}\:{the}\:{other}. \\ $$$${Show}\:{that}\:{c}\left({a}−{b}\right)^{\mathrm{3}} ={a}\left({c}−{b}\right)^{\mathrm{3}} \\ $$$$ \\ $$ Answered by math1967 last updated…