Category: Algebra

Question Number 82191 by jagoll last updated on 19/Feb/20 $$findthesolution$$$$\sqrt{x^2-3x-4}>x-2$$ Commented by arkanmath7@gmail.com last updated on 19/Feb/20 $${x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{4}\:\:\:>\:\:{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{4}…

Question Number 147697 by mathdanisur last updated on 22/Jul/21 $$f\left(0\right)+f\left(1\right)+f\left(2\right)+\dots +f\left(n\right)=n!-n\cdot a$$$$f\left(16\right)=15\cdot (15!-1)$$$$find\mathit{a}=?$$ Answered by Olaf_Thorendsen last updated on 22/Jul/21 $$\underset{{k}=\mathrm{0}} {\overset{{n}}…

Question Number 147689 by mathdanisur last updated on 22/Jul/21 $${\left(234\right)}_5\cdot {\left(23\right)}_5={\left(x\right)}_5\Rightarrow \mathit{x}=?$$ Answered by Olaf_Thorendsen last updated on 22/Jul/21 $$\left(\mathrm{234}\right)_{\mathrm{5}} .\left(\mathrm{23}\right)_{\mathrm{5}} \…

Question Number 147673 by mnjuly1970 last updated on 22/Jul/21 Answered by Rasheed.Sindhi last updated on 22/Jul/21 $$\sqrt[3]{x}+\sqrt[3]{x-2}=\sqrt[3]{x-1}$$$${(\sqrt[3]{x}+\sqrt[3]{x-2})}^3={\left(\sqrt[3]{x-1}\right)}^3$$$$x+x-2+3\sqrt[3]{x}\sqrt[3]{x-2}(\sqrt[3]{x}+\sqrt[3]{x-2})=x-1$$$$\mathrm{3}\sqrt[{\mathrm{3}}]{{x}}\sqrt[{\mathrm{3}}]{{x}−\mathrm{2}}\left(\sqrt[{\mathrm{3}}]{{x}−\mathrm{1}}\right)=−{x}+\mathrm{1} \…

Question Number 82130 by TawaTawa last updated on 18/Feb/20 $$\mathrm{In}\mathrm{an}\mathrm{arrangement}\mathrm{of}\mathrm{the}\mathrm{word}\mathrm{VIOLENT},\mathrm{find}\mathrm{the}\mathrm{chances}$$$$\mathrm{that}\mathrm{the}\mathrm{vowels}\mathrm{I},\mathrm{O},\mathrm{E}\mathrm{occupy}\mathrm{the}\mathrm{odd}\mathrm{positions}.$$ Commented by mr W last updated on 18/Feb/20 $$wehave4oddpositions:1,3,5,7$$$${we}\:{have}\:\mathrm{3}\:{even}\:{positions}:\:\mathrm{2},\:\mathrm{4},\:\mathrm{6}…