Category: Algebra

Question Number 6834 by nburiburu last updated on 30/Jul/16 $${a}\in\mathbb{Z},\:\left(\mathrm{2}{a}^{\mathrm{3}} +\mathrm{3}{a}^{\mathrm{2}} −\mathrm{3}{a}+\mathrm{7}\::\:{a}^{\mathrm{2}} +{a}−\mathrm{2}\right)\neq\mathrm{1}\:\Leftrightarrow\:{a}=\mathrm{3}{k}+\mathrm{1},\:{k}\in\mathbb{Z} \\ $$ Commented by Yozzii last updated on 30/Jul/16 $${All}\:{integers}\:{can}\:{be}\:{written}\:{in}\:{one} \\ $$$${of}\:{the}\:{following}\:{forms}\:{since}…

Question Number 6824 by Tawakalitu. last updated on 30/Jul/16 $${Solve}\:{simultaneously} \\ $$$$\frac{\mathrm{1}}{{u}}\:+\:\frac{\mathrm{1}}{{v}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\:\:……….\:{equation}\:\left({i}\right) \\ $$$$\frac{{u}^{\mathrm{2}} }{{v}}\:+\:\frac{{v}^{\mathrm{2}} }{{u}}\:=\:\mathrm{12}\:\:\:\:\:\:……..\:{equation}\:\left({ii}\right) \\ $$ Commented by sou1618 last updated on 30/Jul/16…

Question Number 6809 by Tawakalitu. last updated on 28/Jul/16 $${If}\:\:{x}^{\frac{\mathrm{1}}{\mathrm{3}}} \:+\:\:{y}^{\frac{\mathrm{1}}{\mathrm{3}}} \:+\:\:{z}^{\frac{\mathrm{1}}{\mathrm{3}}} \:\:=\:\:\mathrm{0},\:\:{Then}\:\:{pove}\:{that}\: \\ $$$$\left({x}\:+\:{y}\:+\:{z}\right)^{\mathrm{3}} \:\:=\:\mathrm{3}{xyz} \\ $$ Commented by Yozzii last updated on 29/Jul/16…

Question Number 72332 by aliesam last updated on 27/Oct/19 $${let}\:{Q}=\frac{\mathrm{1}+{tan}\left(\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\:.\:{tan}\left(\frac{\pi}{\mathrm{10}}\right)}{\mathrm{1}−{tan}\left(\frac{\pi}{\mathrm{8}}\right).{tan}\left(\frac{\pi}{\mathrm{10}}\right)} \\ $$$$ \\ $$$${prove}\:{that} \\ $$$$\: \\ $$$$\frac{{Q}−\mathrm{1}}{{Q}+\mathrm{1}}=\sqrt{\mathrm{7}−\mathrm{3}\sqrt{\mathrm{5}}−\sqrt{\mathrm{85}−\mathrm{38}\sqrt{\mathrm{5}}}} \\ $$$$ \\ $$ Answered by mind…

Question Number 137866 by Yegon last updated on 07/Apr/21 Terms of Service Privacy Policy Contact: info@tinkutara.com