Question Number 176279 by CrispyXYZ last updated on 15/Sep/22 $$\mathrm{Proof}\:\mathrm{that}\:: \\ $$$$\nexists{n}\in\mathbb{Z},\:{n}^{\mathrm{2}} +\mathrm{1}\equiv\mathrm{0}\left(\mathrm{mod}\:\mathrm{4}\right) \\ $$ Answered by mahdipoor last updated on 15/Sep/22 $${I}>\:{n}=\mathrm{2}{k}+\mathrm{1}\: \\ $$$$\Rightarrow{n}^{\mathrm{2}}…
Question Number 45204 by Meritguide1234 last updated on 10/Oct/18 Commented by Tawa1 last updated on 10/Oct/18 $$. \\ $$ Commented by Meritguide1234 last updated on…
Question Number 110728 by Study last updated on 30/Aug/20 $${a}+{b}=\mathrm{9}\:\:,\:\:{ab}=\mathrm{20}\:\:\:\:\:{a}−{b}=? \\ $$ Answered by som(math1967) last updated on 30/Aug/20 $$\left(\mathrm{a}−\mathrm{b}\right)^{\mathrm{2}} =\left(\mathrm{a}+\mathrm{b}\right)^{\mathrm{2}} −\mathrm{4ab} \\ $$$$\left(\mathrm{a}−\mathrm{b}\right)^{\mathrm{2}} =\mathrm{81}−\mathrm{80}…
Question Number 110727 by Study last updated on 30/Aug/20 $${a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{10}\:\:\:,\:\:{ab}=\mathrm{13}\:\:\:,\:{a}^{\mathrm{3}} +{b}^{\mathrm{3}} =? \\ $$ Answered by mr W last updated on 30/Aug/20 $$\left({a}+{b}\right)^{\mathrm{2}}…
Question Number 110725 by Study last updated on 30/Aug/20 $${x}^{{x}^{{x}^{{x}^{…} } } } =\mathrm{2}\:\:\:\:\:\:\:{x}=? \\ $$ Answered by Her_Majesty last updated on 30/Aug/20 $${x}^{{x}^{{x}^{…} }…
Question Number 110715 by Aina Samuel Temidayo last updated on 30/Aug/20 $$\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\:\mathrm{are}\:\mathrm{unit}\:\mathrm{digits}\:\mathrm{whose} \\ $$$$\mathrm{pairwise}\:\mathrm{sums}\:\mathrm{form}\:\mathrm{an}\:\mathrm{arithmetic} \\ $$$$\mathrm{progression}.\:\mathrm{Given}\:\mathrm{that}\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}\:\mathrm{is} \\ $$$$\mathrm{even},\:\mathrm{find}\:\mathrm{the}\:\mathrm{common}\:\mathrm{positive} \\ $$$$\mathrm{difference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{arithmetic} \\ $$$$\mathrm{progression}. \\ $$ Commented…
Question Number 110706 by Aina Samuel Temidayo last updated on 30/Aug/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 45166 by peter frank last updated on 09/Oct/18 Answered by MrW3 last updated on 10/Oct/18 $${N}={number}\:{of}\:{students} \\ $$$${when}\:{the}\:{students}\:{are}\:{divided}\:{into} \\ $$$$\mathrm{12}\:{groups},\:{the}\:{last}\:{group}\:{has}\:\mathrm{5}\:{students}, \\ $$$${i}.{e}.\:{the}\:{other}\:\mathrm{11}\:{groups}\:{have}\:{x}\:{students} \\…
Question Number 110704 by Aina Samuel Temidayo last updated on 30/Aug/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{n}^{\mathrm{2}} +\mathrm{1}}{\mathrm{n}}+\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}},\mathrm{n}>\mathrm{0} \\ $$ Answered by mr W last updated on…
Question Number 110675 by Aina Samuel Temidayo last updated on 30/Aug/20 $$\mathrm{Two}\:\mathrm{polynomials}\:\mathrm{P}\:\mathrm{and}\:\mathrm{Q}\:\mathrm{satisfy} \\ $$$$\mathrm{P}\left(−\mathrm{2x}+\mathrm{Q}\left(\mathrm{x}\right)\right)=\mathrm{Q}\left(−\mathrm{2x}+\mathrm{P}\left(\mathrm{x}\right)\right). \\ $$$$\mathrm{Given}\:\mathrm{that}\:\mathrm{Q}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{4}\:\mathrm{and} \\ $$$$\mathrm{P}\left(\mathrm{x}\right)=\mathrm{ax}+\mathrm{b}.\:\mathrm{Find}\:\mathrm{2a}+\mathrm{b}. \\ $$ Answered by bemath last…