Category: Algebra

Question Number 733 by 123456 last updated on 05/Mar/15 $$\mid \mid \mid \mid \mid \mid \mid x^2-x-1\mid -3\mid -5\mid -7\mid -9\mid -11\mid -13\mid$$$$=x^2-2x-48$$$$findallxrealthatissolutionofabove$$$$equation$$ Answered by prakash jain last…

Question Number 669 by 112358 last updated on 21/Feb/15 $$Givenonlythestandardresult\underset{r=1}{\sum ^N}{r}^2=\frac{1}{6}N(N+1)(2N+1)$$$$isappliedtodeterminingtheseries$$$$\mathrm{1}^{\mathrm{2}} +\mathrm{2}×\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +\mathrm{2}×\mathrm{4}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} +\mathrm{2}×\mathrm{6}^{\mathrm{2}} +\mathrm{7}^{\mathrm{2}} +…+\mathrm{2}\left({n}−\mathrm{1}\right)^{\mathrm{2}} +{n}^{\mathrm{2}}…

Question Number 66197 by Rasheed.Sindhi last updated on 11/Aug/19 $$\mathrm{If}\mathrm{x}+\frac{1}{\mathrm{x}}=1,\mathrm{prove}\mathrm{that}:$$$${\mathrm{x}}^{\mathrm{n}}+{\mathrm{x}}^{\mathrm{n}-2}+{\mathrm{x}}^{\mathrm{n}-4}=0$$ Commented by mr W last updated on 10/Aug/19…

Question Number 131697 by mathlove last updated on 07/Feb/21 $$x^x=6x=?$$ Answered by mr W last updated on 07/Feb/21 $$x=6^{\frac{1}{x}}=e^{\frac{\ln 6}{x}}$$$$\frac{\mathrm{1}}{{x}}{e}^{\frac{\mathrm{ln}\:\mathrm{6}}{{x}}}…

Question Number 131688 by liberty last updated on 07/Feb/21 $$\mathrm{Let}\alpha \mathrm{and}\beta \mathrm{are}\mathrm{the}\mathrm{roots}$$$$\mathrm{of}\mathrm{the}\mathrm{equation}{\mathrm{x}}^2-6\mathrm{x}-2=0.$$$$\mathrm{If}{a}_n={\alpha }^n-{\beta }^n\mathrm{for}n⩾1$$$$\mathrm{then}\mathrm{the}\mathrm{value}\mathrm{of}\frac{a_{10}-2a_8}{2a_9}?$$…