Category: Algebra

Question Number 144468 by mathdanisur last updated on 25/Jun/21 Commented by Rasheed.Sindhi last updated on 26/Jun/21 $${It}^{\prime }ssufficienttosay{}^{\prime }natural{numbers}^{\prime }$$$$insteadof{}^{\prime }positivenatural{numbers}^{\prime }.$$ Terms of Service Privacy…

Question Number 78931 by mr W last updated on 21/Jan/20 $$ifx+\frac{1}{x}=a$$$$find{x}^n+\frac{1}{x^n}=?$$ Commented by mathmax by abdo last updated on…

Question Number 13391 by Tinkutara last updated on 19/May/17 $$\mathrm{A}\mathrm{four}\mathrm{digit}\mathrm{number}\mathrm{has}\mathrm{the}\mathrm{following}$$$$\mathrm{properties}:$$$$\left(\mathrm{a}\right)\mathrm{It}\mathrm{is}\mathrm{a}\mathrm{perfect}\mathrm{square}$$$$\left(\mathrm{b}\right)\mathrm{The}\mathrm{first}\mathrm{two}\mathrm{digits}\mathrm{are}\mathrm{equal}$$$$\left(\mathrm{c}\right)\mathrm{The}\mathrm{last}\mathrm{two}\mathrm{digits}\mathrm{are}\mathrm{equal}.$$$$\mathrm{Find}\mathrm{all}\mathrm{such}\mathrm{numbers}.$$ Answered by RasheedSindhi…

Question Number 13388 by Tinkutara last updated on 19/May/17 $$\mathrm{Find}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{all}\mathrm{rational}\mathrm{numbers}$$$$\frac{m}{n}\mathrm{such}\mathrm{that}\left(\mathrm{i}\right)0<\frac{m}{n}<1,\left(\mathrm{ii}\right)m\mathrm{and}$$$$n\mathrm{are}\mathrm{relatively}\mathrm{prime}\mathrm{and}\left(\mathrm{iii}\right)mn=25!.$$ Commented by RasheedSindhi last updated on 19/May/17 $$\mathrm{There}\:\mathrm{is}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{such}\:\mathrm{number}: \…

Question Number 13377 by tawa tawa last updated on 19/May/17 Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 19/May/17 $${(x+\frac{1}{x})}^2-{(x-\frac{1}{x})}^2=4\Rightarrow x-\frac{1}{x}=\pm i\sqrt{3}$$$$\{\begin{array}{l}x-\frac{1}{x}=\pm i\sqrt{3}\\ x+\frac{1}{x}=-1\end{array}\Rightarrow x=\frac{-1\pm i\sqrt{3}}{2}$$$${x}^{\mathrm{2}} =−{x}−\mathrm{1}…