Question Number 179900 by Shrinava last updated on 03/Nov/22 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{f}\:=\:\mathrm{5x}^{\mathrm{4}} \:+\:\mathrm{35x}^{\mathrm{3}} \:+\:\mathrm{28x}^{\mathrm{2}} \:+\:\mathrm{14x}\:+\:\mathrm{7}\:\:\mathrm{is}\:\mathrm{irreducible}\:\mathrm{in}\:\:\mathrm{Q}\left[\mathrm{x}\right] \\ $$ Answered by floor(10²Eta[1]) last updated on 04/Nov/22 $$\mathrm{we}\:\mathrm{want}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{p}\:\mathrm{such}\:\mathrm{that}…
Question Number 179890 by mr W last updated on 03/Nov/22 $${p}\left({x}\right)=\left(\mathrm{1}−{x}\right)\left(\mathrm{1}+\mathrm{2}{x}\right)\left(\mathrm{1}−\mathrm{3}{x}\right)….\left(\mathrm{1}−\mathrm{15}{x}\right) \\ $$$$ \\ $$$${find}\:{the}\:{coefficient}\:{of}\:{the}\:{x}^{\mathrm{3}} \:{term} \\ $$$${in}\:{the}\:{expansion}. \\ $$ Commented by mr W last…
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Question Number 48795 by rahul 19 last updated on 28/Nov/18 $${Find}\:{the}\:{sum}: \\ $$$$\:^{\mathrm{30}} {C}_{\mathrm{0}} .\mathrm{5}^{\mathrm{100}} −^{\mathrm{30}} {C}_{\mathrm{1}} .\mathrm{5}^{\mathrm{98}} .\mathrm{3}^{\mathrm{3}} +^{\mathrm{30}} {C}_{\mathrm{2}} .\mathrm{5}^{\mathrm{96}} .\mathrm{3}^{\mathrm{6}} −\:…=? \\…
Question Number 179819 by caquito last updated on 02/Nov/22 $${x}+{y}+{z}=\mathrm{2} \\ $$$${x}+\mathrm{2}{y}−{z}=\mathrm{4} \\ $$$$\mathrm{2}{x}+{y}−\mathrm{2}{z}=\mathrm{2} \\ $$$$ \\ $$ Answered by manxsol last updated on 03/Nov/22…
Question Number 179781 by Ari last updated on 02/Nov/22 Commented by Ari last updated on 02/Nov/22 who can solve it? Commented by MJS_new last updated on 02/Nov/22 $$\mathrm{who}\:\mathrm{cannot}\:\mathrm{solve}\:\mathrm{it}?…
Question Number 48705 by rahul 19 last updated on 27/Nov/18 $${Q}.\mathrm{1}\rightarrow \\ $$$${Coefficient}\:{of}\:{a}^{\mathrm{8}} {b}^{\mathrm{4}} {c}^{\mathrm{9}} {d}^{\mathrm{9}} \:{in}\:{expansion} \\ $$$${of}\:\left({abc}+{abd}+{acd}+{bcd}\right)^{\mathrm{10}} \:=? \\ $$$$ \\ $$$${Q}.\mathrm{2}\rightarrow \\…
Question Number 179777 by luciferit last updated on 02/Nov/22 $${p}\left({x}\right)=\left(\mathrm{1}−{x}\right)\left(\mathrm{1}+\mathrm{2}{x}\right)\left(\mathrm{1}−\mathrm{3}{x}\right)….\left(\mathrm{1}+\mathrm{14}{x}\right)\left(\mathrm{1}−\mathrm{15}{x}\right) \\ $$$$ \\ $$$${the}\:{absolute}\:{value}\:{of}\:{the}\:{coefficient}\:{of}\:{the}\:{x}^{\mathrm{2}} \:{in}\:{the}\:{expression}? \\ $$ Answered by mr W last updated on 02/Nov/22…
Question Number 179773 by Acem last updated on 02/Nov/22 $${What}'{s}\:{the}\:{sum}\:{of}\:{the}\:{odd}\:{numbers} \\ $$$$\:{between}\:\mathrm{2313}\:{and}\:\mathrm{4718} \\ $$ Commented by CElcedricjunior last updated on 05/Nov/22 $$\boldsymbol{{calculons}}\:\boldsymbol{{la}}\:\boldsymbol{{somme}}\:\boldsymbol{{des}}\:\boldsymbol{{nombres}} \\ $$$$\boldsymbol{{comprises}}\:\boldsymbol{{entre}}\:\mathrm{2313}\:\boldsymbol{{et}}\:\mathrm{4718} \\…
Question Number 179775 by Acem last updated on 02/Nov/22 $$\:\left(\mathrm{122}−{a}\right)^{\mathrm{2}} =\:\left(\mathrm{123}−{a}\right)^{\mathrm{2}} \\ $$ Answered by Rasheed.Sindhi last updated on 02/Nov/22 $$\:\left(\mathrm{122}−{a}\right)^{\mathrm{2}} =\:\left(\mathrm{123}−{a}\right)^{\mathrm{2}} \\ $$$$\:\left(\mathrm{122}−{a}\right)^{\mathrm{2}} −\:\left(\mathrm{122}−{a}+\mathrm{1}\right)^{\mathrm{2}}…