Category: Algebra

Question Number 195898 by Calculusboy last updated on 12/Aug/23 Answered by qaz last updated on 13/Aug/23 $${a}_{{n}+\mathrm{2}} {a}_{{n}+\mathrm{1}} −{a}_{{n}+\mathrm{1}} {a}_{{n}} =\mathrm{2}\:\:\:\:\Rightarrow{a}_{{n}+\mathrm{2}} {a}_{{n}+\mathrm{1}} =\mathrm{2}{n}+{a}_{\mathrm{1}} {a}_{\mathrm{2}} =\mathrm{2}\left({n}+\mathrm{1}\right)…

Question Number 195855 by jabarsing last updated on 11/Aug/23 $$\{\begin{array}{l}3\sqrt{\sqrt[3]{12}-\sqrt[3]{3}}=\sqrt[3]{x}+\sqrt[3]{y}-\sqrt[3]{z}\\ x,y,z\in N\end{array}\Rightarrow x,y,z=?$$$$pleasehelpme$$ Answered by Rasheed.Sindhi last updated on 13/Aug/23 $$\mathrm{Unsuccessful}\mathrm{Try}\dots$$$$$$\{\begin{array}{l}3\sqrt{\sqrt[3]{12}-\sqrt[3]{3}}=\sqrt[3]{x}+\sqrt[3]{y}-\sqrt[3]{z}\\ x,y,z\in N\end{array}$$\:\:\Rightarrow\:{x},{y},{z}\:=? \…

Question Number 195809 by mr W last updated on 11/Aug/23 $$if{x}^5+x+1=0,find{x}^3-x^2=?$$ Commented by jabarsing last updated on 11/Aug/23 $${hello}\:{dear}\:{W}, \…

Question Number 195733 by York12 last updated on 09/Aug/23 $$provethat$$$$\underset{n=2}{\sum ^{\mathrm{\infty }}}\left[\frac{B_{\stackrel{\mathrm{\_}}{n}}}{(n-2)!}\right]=\frac{e(3-e)}{{(e-1)}^3}$$$$where{B}_{\stackrel{\mathrm{\_}}{n}}isthen-th{bernouli}^{\prime }snumber$$ Answered by…

Question Number 195689 by Shomurotovdiyorbek last updated on 07/Aug/23 $$\int_{\mathrm{1}} ^{\mathrm{3}} {f}\left({x}\right)^{\mathrm{3}} {f}'\left({x}\right){dx}=\int_{\mathrm{1}} ^{\mathrm{3}} \left({f}\left({x}\right)^{\mathrm{3}} \right){df}\left({x}\right)=\int_{\mathrm{1}} ^{\mathrm{3}} {t}^{\mathrm{3}} {dt}=\frac{{t}^{\mathrm{4}} }{\mathrm{4}}\int_{\mathrm{1}} ^{\mathrm{3}} =\frac{{f}\left({x}\right)^{\mathrm{4}} }{\mathrm{4}}\int_{\mathrm{1}} \mathrm{3} \…