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Category: Algebra

Question-147103

Question Number 147103 by mnjuly1970 last updated on 18/Jul/21 Answered by mr W last updated on 18/Jul/21 $${x}={n}+{f},\:{n}\in{Z},\:\mathrm{0}\leqslant{f}<\mathrm{1} \\ $$$${x}^{\mathrm{2}} =\left({n}+{f}\right)^{\mathrm{2}} ={n}^{\mathrm{2}} +{f}^{\mathrm{2}} +\mathrm{2}{nf} \\…

Question-16000

Question Number 16000 by tawa tawa last updated on 16/Jun/17 Answered by mrW1 last updated on 16/Jun/17 $$\mathrm{I}\:\mathrm{assume}\:\mathrm{you}\:\mathrm{mean}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{roots}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{tan}\:\theta\:+\:\mathrm{b}\:\mathrm{sec}\:\theta\:=\:\mathrm{c} \\ $$$$ \\ $$$$\mathrm{a}\:\mathrm{tan}\:\theta\:+\:\mathrm{b}\:\mathrm{sec}\:\theta\:=\:\mathrm{c} \\…

x-3-2-1-solve-for-real-x-

Question Number 81519 by ajfour last updated on 13/Feb/20 $$\mid\mid\mid{x}\mid−\mathrm{3}\mid−\mathrm{2}\mid=\mathrm{1} \\ $$$${solve}\:{for}\:{real}\:{x}. \\ $$ Commented by mr W last updated on 13/Feb/20 $$\mid\mid\mid{x}\mid−\mathrm{3}\mid−\mathrm{2}\mid=\mathrm{1} \\ $$$$\mid\mid{x}\mid−\mathrm{3}\mid−\mathrm{2}=\pm\mathrm{1}…

Question-81506

Question Number 81506 by Power last updated on 13/Feb/20 Commented by Power last updated on 13/Feb/20 $$\left.\mathrm{A}\left.\right)\left.\mathrm{1}\left.−\frac{\mathrm{1}}{\mathrm{50}!}\:\:\:\:\:\:\:\mathrm{B}\right)\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\mathrm{C}\right)\mathrm{1}+\frac{\mathrm{1}}{\mathrm{49}!}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{D}\right)\mathrm{2} \\ $$ Commented by mr W last updated…

Question-81507

Question Number 81507 by Power last updated on 13/Feb/20 Commented by mr W last updated on 13/Feb/20 $${we}\:{have}\:\frac{\mathrm{2}{n}+\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} }=\frac{\mathrm{1}}{{n}^{\mathrm{2}} }−\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$ \\…