Category: Algebra

Question Number 155500 by VIDDD last updated on 01/Oct/21 Answered by MJS_new last updated on 01/Oct/21 $$f(x+y)-(f\left(x\right)+f\left(y\right))=0$$$$2axy-c=0$$$$\mathrm{this}\mathrm{is}\mathrm{only}\mathrm{true}\mathrm{\forall }x,y\in \mathbb{R}\mathrm{with}a=0\Rightarrow c=0$$$$a+b+c=3\Rightarrow b=3$$$${f}\left({x}\right)=\mathrm{3}{x}…

Question Number 155497 by VIDDD last updated on 01/Oct/21 Answered by amin96 last updated on 01/Oct/21 $$\sqrt{4-\frac{1}{3\sqrt{2}}\underbrace{\sqrt{4-\frac{1}{3\sqrt{2}}\dots }}}=\mathbf{x}$$$$\sqrt{4-\frac{1}{3\sqrt{2}}\mathbf{x}}=\mathbf{x}\Rightarrow {\mathbf{x}}^2=4-\frac{\mathbf{x}}{3\sqrt{2}}\Rightarrow 3{\mathbf{x}}^2\sqrt{2}+\mathbf{x}-12\sqrt{2}=0$$$$\mathbf{\Delta }=289\mathbf{x}=\frac{-1+17}{6\sqrt{2}}=\frac{8}{3\sqrt{2}}$$$$\boldsymbol{\mathrm{A}}=\mathrm{10}+\boldsymbol{\mathrm{log}}_{\frac{\mathrm{3}}{\mathrm{2}}}…

Question Number 89955 by swizanjere@gmail.com last updated on 20/Apr/20 $$9^{\mathrm{x}+1}\nmid 28\left(3^{\mathrm{x}}\right)+3=0$$ Commented by jagoll last updated on 20/Apr/20 $$\mathrm{what}\mathrm{do}\mathrm{you}\mathrm{mean}\mathrm{notation}$$$$\nmid\:? \…

Question Number 155480 by mathdanisur last updated on 01/Oct/21 $$\mathrm{Find}\mathrm{the}\mathrm{positive}\mathrm{integer}\mathrm{solution}$$$$\mathrm{of}\mathrm{the}\mathrm{equation}:$$$${\mathrm{x}}^3+{\mathrm{y}}^3=911(\mathrm{xy}+49)$$ Answered by Rasheed.Sindhi last updated on 01/Oct/21…

Question Number 89938 by jagoll last updated on 20/Apr/20 $$\mathrm{If}\mathrm{x}(\mathrm{x}+1)=1$$$$\mathrm{find}{(\mathrm{x}+1)}^3-\frac{1}{{(\mathrm{x}+1)}^3}$$ Commented by john santu last updated on 20/Apr/20 $${let}\:{x}+\mathrm{1}=\:{t}\:\Rightarrow{x}\:=\:{t}−\mathrm{1}…