Question Number 150883 by mathdanisur last updated on 16/Aug/21 $$\mathrm{prove}\:\mathrm{that}\:\mathrm{any}\:\mathrm{real}\:\mathrm{root}\:\boldsymbol{\alpha}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}:\:\:\mathrm{x}^{\mathrm{6}\boldsymbol{\mathrm{n}}} \:=\:\mathrm{4x}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \:+\:\mathrm{4}\:;\:\mathrm{n}\in\mathbb{N}-\left\{\mathrm{0}\right\} \\ $$$$\mathrm{verify}:\:\:\mid\boldsymbol{\alpha}\mid\:>\:\sqrt[{\mathrm{2}\boldsymbol{\mathrm{n}}}]{\mathrm{2}} \\ $$ Answered by mindispower last updated on 16/Aug/21…
Question Number 19799 by Tinkutara last updated on 15/Aug/17 $$\mathrm{For}\:\mathrm{a}\:\mathrm{natural}\:\mathrm{number}\:{b},\:\mathrm{let}\:{N}\left({b}\right)\:\mathrm{denote} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{natural}\:\mathrm{numbers}\:{a}\:\mathrm{for} \\ $$$$\mathrm{which}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} \:+\:{ax}\:+\:{b}\:=\:\mathrm{0}\:\mathrm{has} \\ $$$$\mathrm{integer}\:\mathrm{roots}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{smallest} \\ $$$$\mathrm{value}\:\mathrm{of}\:{b}\:\mathrm{for}\:\mathrm{which}\:{N}\left({b}\right)\:=\:\mathrm{20}? \\ $$ Commented by dioph last…
Question Number 150870 by liberty last updated on 16/Aug/21 Commented by mnjuly1970 last updated on 16/Aug/21 $$\:\:{pls}\:\:{solve}\:{it}… \\ $$ Answered by tabata last updated on…
Question Number 150865 by Tawa11 last updated on 16/Aug/21 Im{f'(z)} = 6x(2y-1) and f(0) = 3 – 2i, f(1) = 6 – 5i. Find f(2…
Question Number 85322 by mathocean1 last updated on 20/Mar/20 $${please}\:{help}\:{me}\:{to}\:{solve}\:{this}\:{in}\:\mathbb{N} \\ $$$${A}_{{n}} ^{\mathrm{2}} −\mathrm{3}{C}_{{n}} ^{\:{n}−\mathrm{2}} +{n}=−\mathrm{20} \\ $$ Commented by mr W last updated on…
Question Number 19785 by Tinkutara last updated on 15/Aug/17 $$\mathrm{If}\:{x}^{\left({x}^{\mathrm{4}} \right)} \:=\:\mathrm{4},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${x}^{\left({x}^{\mathrm{2}} \right)} \:+\:{x}^{\left({x}^{\mathrm{8}} \right)} ? \\ $$ Answered by Tinkutara last updated…
Question Number 19786 by Tinkutara last updated on 15/Aug/17 $$\mathrm{For}\:\mathrm{natural}\:\mathrm{numbers}\:{x}\:\mathrm{and}\:{y},\:\mathrm{let}\:\left({x},\:{y}\right) \\ $$$$\mathrm{denote}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{common}\:\mathrm{divisor}\:\mathrm{of} \\ $$$${x}\:\mathrm{and}\:{y}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{natural} \\ $$$$\mathrm{numbers}\:{x}\:\mathrm{and}\:{y}\:\mathrm{with}\:{x}\:\leqslant\:{y}\:\mathrm{satisfy}\:\mathrm{the} \\ $$$$\mathrm{equation}\:{xy}\:=\:{x}\:+\:{y}\:+\:\left({x},\:{y}\right)? \\ $$ Answered by mrW1 last updated…
Question Number 150853 by mathdanisur last updated on 15/Aug/21 $$\mathrm{log}_{\mathrm{2021}} \:\sqrt{\mathrm{x}\::\:\sqrt{\mathrm{x}\::\:\sqrt{\mathrm{x}\::..}}}\:=\:\mathrm{674} \\ $$$$\mathrm{find}\:\:\boldsymbol{\mathrm{x}}=? \\ $$ Commented by liberty last updated on 16/Aug/21 $$\sqrt{\frac{\mathrm{x}}{\:\sqrt{\frac{\mathrm{x}}{\:\sqrt{\frac{\mathrm{x}}{\:\sqrt{\frac{\mathrm{x}}{\vdots}}}}}}}}\:=\:\mathrm{2021}^{\mathrm{674}} \\ $$$$\Leftrightarrow\sqrt{\frac{\mathrm{x}}{\mathrm{2021}^{\mathrm{674}}…
Question Number 85318 by Power last updated on 20/Mar/20 Commented by Power last updated on 21/Mar/20 $$+\mathrm{R}\left(\mathrm{x}\right)\:\:\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 150852 by mathdanisur last updated on 15/Aug/21 $$\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{3}\:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{xyz}\:\leqslant\:\left(\frac{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:-\:\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \:\leqslant\:\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com