Category: Algebra

Question Number 73035 by mathmax by abdo last updated on 05/Nov/19 $$provethat\mathrm{\forall }n\in N^{★}2!4!\dots .\left(2n\right)!⩾{\{(n+1)!\}}^n$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 73031 by mathmax by abdo last updated on 05/Nov/19 $$solveinside{N}^{2}3x^3+xy+4y^3=349$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 73029 by mathmax by abdo last updated on 05/Nov/19 $$provethat\mathrm{\forall }(n,p,q)\in N^3\sum _{k=0}^n{C}_p^k{C}_q^{n-k}=C_{p+q}^n$$$${conclude}\:{that}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\left({C}_{{n}} ^{{k}}…

Question Number 73027 by mathmax by abdo last updated on 05/Nov/19 $$xandyarereals\left(orcomplex\right)letput{x}^{\left(0\right)}=1,x^{\left(1\right)}=x$$$$x^{\left(2\right)}=x(x-1)\dots ..x^{\left(n\right)}=x(x-1)(x-2)\dots (x-n+1)provethat$$$$\left({x}+{y}\right)^{\left({n}\right)} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:\:{x}^{\left({n}−{k}\right)}…

Question Number 7478 by Yozzia last updated on 31/Aug/16 $$Findthevalueof{x}^3(x^3-18)ifx(x-3)=-1.$$ Answered by Rasheed Soomro last updated on 31/Aug/16 $$\:\:\:{x}^{\mathrm{3}} \left({x}^{\mathrm{3}} −\mathrm{18}\right)\:\:{if}\:\:{x}\left({x}−\mathrm{3}\right)=−\mathrm{1}…