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Category: Arithmetic

Question-46383

Question Number 46383 by peter frank last updated on 24/Oct/18 Commented by maxmathsup by imad last updated on 24/Oct/18 $${z}=\mathrm{0}\:{is}\:{not}\:{solution}\:{for}\:{z}\neq\mathrm{0}\:\:\left({e}\right)\:\Leftrightarrow\:\left(\frac{{z}+\mathrm{1}}{{z}}\right)^{{n}} =\mathrm{1}\:\Leftrightarrow\left(\mathrm{1}+{z}^{−\mathrm{1}} \right)^{{n}} =\mathrm{1}\:\:{the}\:{roots}\:{of} \\ $$$${Z}^{{n}}…

Question-46358

Question Number 46358 by peter frank last updated on 24/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 24/Oct/18 $$\left.{b}\right)\left({x}+{y}\right)^{\mathrm{2}} \left({xdy}+{ydx}\right)={xy}\left({dx}+{dy}\right) \\ $$$$\left({x}+{y}\right)^{\mathrm{2}} {d}\left({xy}\right)={xy}\left({dx}+{dy}\right) \\ $$$$\frac{{d}\left({xy}\right)}{{xy}}=\frac{{d}\left({x}+{y}\right)}{\left({x}+{y}\right)^{\mathrm{2}} }…

Question-46168

Question Number 46168 by peter frank last updated on 21/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 22/Oct/18 $$\mathrm{1}+{w}+{w}^{\mathrm{2}} =\mathrm{0}\:\:\:{w}^{\mathrm{3}} =\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\left(−{w}^{\mathrm{2}} −{w}^{\mathrm{2}} \right)^{\mathrm{3}} −\left(−{w}−{w}\right)^{\mathrm{3}}…

Question-46083

Question Number 46083 by peter frank last updated on 20/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 21/Oct/18 $$\alpha^{\mathrm{7}} =\mathrm{1} \\ $$$$\alpha^{\mathrm{7}} −\mathrm{1}=\mathrm{0} \\ $$$$\left(\alpha−\mathrm{1}\right)\left(\alpha^{\mathrm{6}} +\alpha^{\mathrm{5}}…

Find-the-sum-k-1-n-tan-1-2k-2-k-2-k-4-Answer-tan-1-n-2-n-1-pi-4-

Question Number 46032 by Tawa1 last updated on 20/Oct/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}:\:\:\:\:\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\:\mathrm{tan}^{−\mathrm{1}} \:\left(\frac{\mathrm{2k}}{\mathrm{2}\:+\:\mathrm{k}^{\mathrm{2}} \:+\:\mathrm{k}^{\mathrm{4}} }\right) \\ $$$$ \\ $$$$\mathrm{Answer}:\:\:\:\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{n}^{\mathrm{2}} \:+\:\mathrm{n}\:+\:\mathrm{1}\right)\:−\:\frac{\pi}{\mathrm{4}} \\ $$ Answered by…

In-a-geometric-sequence-of-real-numbers-the-sum-of-the-first-two-terms-is-7-and-the-sum-of-the-first-six-terms-is-91-The-sum-of-the-first-four-terms-is-

Question Number 111542 by Aina Samuel Temidayo last updated on 04/Sep/20 $$\mathrm{In}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{sequence}\:\mathrm{of}\:\mathrm{real} \\ $$$$\mathrm{numbers},\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{two}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{7}\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{six}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{91}.\:\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{four}\:\mathrm{terms}\:\mathrm{is}. \\ $$$$ \\ $$ Commented…

Question-177005

Question Number 177005 by Ar Brandon last updated on 29/Sep/22 Answered by Rasheed.Sindhi last updated on 29/Sep/22 $$\mathrm{3}{x}+\mathrm{7}\equiv\mathrm{12}\left[\mathrm{29}\right] \\ $$$$\mathrm{3}{x}\equiv\mathrm{5}+\mathrm{29}×\mathrm{2}\left[\mathrm{29}\right] \\ $$$$\mathrm{3}{x}\equiv\mathrm{63}\left[\mathrm{29}\right] \\ $$$${x}=\mathrm{21}\left[\mathrm{29}\right] \\…