Category: Algebra

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}…

Question Number 144446 by mathdanisur last updated on 25/Jun/21 Answered by Rasheed.Sindhi last updated on 26/Jun/21 $$2sin(A+60)sin(B+60)cosC$$$$={sin}^2(C+60)$$$$A=180-(B+C)$$$${sin}\left({A}+\mathrm{60}\right)={sin}\left(\:\mathrm{180}−\left({B}+{C}\right)\:\right) \…

Question Number 144421 by loveineq last updated on 25/Jun/21 $$\mathrm{Let}a,b,c>0\mathrm{and}a+b+c=3.\mathrm{Prove}\mathrm{that}$$$$\frac{a^{2021}+b^{2021}+c^{2021}}{3}⩾1+\frac{4042}{3}(1-\frac{ab+bc+ca}{3})$$ Terms of Service Privacy Policy Contact: info@tinkutara.com