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Category: Algebra

determinant-23-23-1-1-2-2-3-3-21-21-

Question Number 194135 by cortano12 last updated on 28/Jun/23 $$\:\:\:\:\:\:\begin{array}{|c|}{\frac{\mathrm{23}!−\mathrm{23}}{\mathrm{1}.\mathrm{1}!+\mathrm{2}.\mathrm{2}!+\mathrm{3}.\mathrm{3}!+…+\mathrm{21}.\mathrm{21}!}\:=?}\\\hline\end{array} \\ $$ Answered by Frix last updated on 28/Jun/23 $$\mathrm{23} \\ $$$$\left[\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}{j}×{j}!=\left({n}+\mathrm{1}\right)!−\mathrm{1}\right] \\…

Question-194113

Question Number 194113 by Rupesh123 last updated on 28/Jun/23 Answered by Subhi last updated on 28/Jun/23 $$ \\ $$$$\frac{{a}\left({a}−\mathrm{1}\right)\left({a}−\mathrm{2}\right)…..}{{a}\left({a}−\mathrm{2}\right)\left({a}−\mathrm{4}\right)…..}.\frac{{b}\left({b}−\mathrm{2}\right)\left({b}−\mathrm{4}\right)…}{{b}\left({b}−\mathrm{1}\right)\left({b}−\mathrm{2}\right)….} \\ $$$$\:=\:\frac{\left({a}−\mathrm{1}\right)\left({a}−\mathrm{3}\right)\left({a}−\mathrm{5}\right)…..}{\left({b}−\mathrm{1}\right)\left({b}−\mathrm{3}\right)\left({b}−\mathrm{5}\right)…..}\:\:\:\: \\ $$$$\mathrm{24}\:{can}\:{be}\:{the}\:{multiplication}\:{of}\:{n},\:{n}+\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{4}\right),\left(\mathrm{6}\right)…

Question-194216

Question Number 194216 by Rupesh123 last updated on 30/Jun/23 Answered by qaz last updated on 01/Jul/23 $$\begin{pmatrix}{\mathrm{2084}}\\{\mathrm{1042}}\end{pmatrix}=\begin{pmatrix}{\mathrm{4}×\mathrm{521}}\\{\mathrm{2}×\mathrm{521}}\end{pmatrix}\equiv\begin{pmatrix}{\mathrm{4}}\\{\mathrm{2}}\end{pmatrix}\equiv\mathrm{6}\left({mod}\:\mathrm{521}\right) \\ $$ Terms of Service Privacy Policy Contact:…

Question-194219

Question Number 194219 by Shlock last updated on 30/Jun/23 Answered by Frix last updated on 30/Jun/23 $$\left({x}^{\mathrm{3}} +\mathrm{4}{x}−\mathrm{8}\right)\left({x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{8}\right)\left({x}+\mathrm{2}\right)= \\ $$$$={x}^{\mathrm{7}} +\mathrm{64}{x}^{\mathrm{2}} −\mathrm{128} \\…

1-kx-1-3-x-1-has-two-real-roots-k-kx-1-1-3x-3x-2-x-3-x-3-3x-2-k-3-x-0-x-0-x-2-3x-k-3-0-1-0-9-4k-12-0-

Question Number 194209 by mnjuly1970 last updated on 01/Jul/23 $$ \\ $$$$\:\:\:\:\:\:\sqrt[{\mathrm{3}}]{\mathrm{1}+{kx}}\:+{x}\:=\:\mathrm{1}\:\:\:{has} \\ $$$$\:\:\:\:\:\:{two}\:{real}\:{roots}\:.\:\:\Rightarrow\:{k}=? \\ $$$$\:\:\:{kx}+\mathrm{1}=\:\mathrm{1}−\mathrm{3}{x}+\mathrm{3}{x}^{\mathrm{2}} −{x}^{\:\mathrm{3}} \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:{x}^{\:\mathrm{3}} \:−\mathrm{3}{x}^{\:\mathrm{2}} +\:\left({k}+\mathrm{3}\right){x}=\mathrm{0} \\ $$$$\:\:\:\:\:{x}=\mathrm{0}…

Question-194204

Question Number 194204 by Rupesh123 last updated on 30/Jun/23 Answered by MM42 last updated on 30/Jun/23 $${if}\:\:{n}={m}=\mathrm{0}\Rightarrow\mathrm{2}{a}_{\mathrm{0}} −\mathrm{1}=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{2}{a}_{\mathrm{0}} \right)\Rightarrow{a}_{\mathrm{0}} =\mathrm{1} \\ $$$${if}\:\:{m}=\mathrm{1}\:,\:{n}=\mathrm{0}\Rightarrow\mathrm{2}{a}_{\mathrm{1}} −\mathrm{2}=\frac{\mathrm{1}}{\mathrm{2}}\left({a}_{\mathrm{2}} +{a}_{\mathrm{0}} \right)…