Category: Algebra

Question Number 22316 by Tinkutara last updated on 15/Oct/17 $$\mathrm{Prove}\mathrm{that}\mathrm{the}\mathrm{coefficient}\mathrm{of}{x}^p\mathrm{in}\mathrm{the}$$$$\mathrm{expansion}\mathrm{of}{(a_0+a_{1}x+a_2{x}^2+a_3{x}^3+\dots +a_k{x}^k)}^n$$$$\mathrm{is}\:\Sigma\frac{{n}!}{{n}_{\mathrm{0}} !{n}_{\mathrm{1}} !{n}_{\mathrm{2}}…

Question Number 153381 by mathdanisur last updated on 06/Sep/21 $$\mathrm{let}\mathrm{x};\mathrm{y};\mathrm{z}⩾0\mathrm{and}{\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2=12$$$$\mathrm{find}\mathrm{the}\min \mathrm{value}\mathrm{of}$$$$\mathrm{S}=\mathrm{x}+\mathrm{y}+\mathrm{z}+\mathrm{xyz}+\frac{1}{\mathrm{xy}+\mathrm{yz}+\mathrm{zx}}$$ Commented by mr W last updated…

Question Number 87817 by M±th+et£s last updated on 06/Apr/20 $$f\left(\frac{x-3}{x+1}\right)+f\left(\frac{x+3}{x-1}\right)=x$$$$findf\left(x\right)$$ Commented by M±th+et£s last updated on 06/Apr/20 $$like87755questionbuthere(x-1)$$ Commented…

Question Number 22244 by ajfour last updated on 14/Oct/17 $$Solvetheinequality:$$$$-9\left(\sqrt[4]{x}\right)+\sqrt{x}+18⩾0.$$ Answered by $@ty@mlastupdatedon14/Oct/17$$Let\sqrt{x}=y$$$$−\mathrm{9}\sqrt{{y}}+{y}+\mathrm{18}\geqslant\mathrm{0} \…

Question Number 87755 by john santu last updated on 06/Apr/20 $$\mathrm{f}\left(\frac{\mathrm{x}-3}{\mathrm{x}+1}\right)+\mathrm{f}\left(\frac{\mathrm{x}+3}{1-\mathrm{x}}\right)=\mathrm{x}$$$$\mathrm{find}\mathrm{f}\left(\mathrm{x}\right)$$ Commented by john santu last updated on 06/Apr/20 $$\left(\mathrm{i}\right)\:\mathrm{let}\:\frac{\mathrm{x}−\mathrm{3}}{\mathrm{x}+\mathrm{1}}\:=\:\mathrm{x}'\:\Rightarrow\mathrm{f}\left(\mathrm{x}'\right)\:+\:\mathrm{f}\left(\frac{\mathrm{x}'−\mathrm{3}}{\mathrm{x}'+\mathrm{1}}\right)\:=\:\frac{\mathrm{x}'+\mathrm{3}}{\mathrm{1}−\mathrm{x}} \…