Category: Algebra

Question Number 58410 by Tawa1 last updated on 22/Apr/19 $$\mathrm{Show}\mathrm{that}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{cube}\mathrm{of}\mathrm{three}\mathrm{consecutive}$$$$\mathrm{number}\mathrm{gives}\mathrm{a}\mathrm{multiple}\mathrm{of}9.$$ Answered by mr W last updated on 22/Apr/19 $${S}=\left({n}−\mathrm{1}\right)^{\mathrm{3}} +{n}^{\mathrm{3}} +\left({n}+\mathrm{1}\right)^{\mathrm{3}}…

Question Number 58402 by rahul 19 last updated on 22/Apr/19 $$Theimaginarypartof{(\frac{1}{2}+\frac{1}{2}i)}^{10}is?$$ Commented by maxmathsup by imad last updated on 23/Apr/19 $${let}\:{Z}\:=\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}{i}\right)^{\mathrm{10}} \:\Rightarrow{Z}\:=\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{10}}…

Question Number 58390 by MJS last updated on 22/Apr/19 $$\mathrm{write}\mathrm{without}\mathrm{roots}\mathrm{in}\mathrm{denominator}\mathrm{if}\mathrm{possible}$$$$\left(1\right)\frac{1}{\sqrt{a}}$$$$\left(2\right)\frac{1}{\sqrt{a}+\sqrt{b}}$$$$\left(3\right)\frac{1}{\sqrt{a}+\sqrt{b}+\sqrt{c}}$$$$\left(4\right)\frac{1}{\sqrt{a}+\sqrt{b}+\sqrt{c}+\sqrt{d}}$$$$\left(5\right)\frac{1}{\sqrt{a}+\sqrt{b}+\sqrt{c}+\sqrt{d}+\sqrt{e}}$$ Commented by tanmay…

Question Number 189446 by mathlove last updated on 16/Mar/23 $$x^2=\sqrt[5]{2}+y$$$$y^2=\sqrt[5]{2}+x$$$$x\cdot y=?x\ne y$$ Answered by cortano12 last updated on 16/Mar/23…

Question Number 123886 by Ar Brandon last updated on 29/Nov/20 $$\mathrm{Let}\stackrel{-}{lz}+l\stackrel{-}{z}+m=0\mathrm{be}\mathrm{a}\mathrm{straight}\mathrm{line}\mathrm{in}\mathrm{the}\mathrm{complex}\mathrm{plane}$$$$\mathrm{and}P\left(z_0\right)\mathrm{be}\mathrm{a}\mathrm{point}\mathrm{in}\mathrm{the}\mathrm{plane}.\mathrm{Then}\mathrm{the}\mathrm{equation}$$$$\mathrm{of}\mathrm{the}\mathrm{line}\mathrm{passing}\mathrm{through}P\left(z_0\right)\mathrm{and}\mathrm{perpendicular}$$$$\mathrm{to}\mathrm{the}\mathrm{given}\mathrm{line}\mathrm{is}\mathrm{\_}\mathrm{\_}\mathrm{\_}$$ Answered by…