Category: Algebra

Question Number 15504 by rish@bh last updated on 11/Jun/17 $$\mathrm{Solve}\lceil x^2\rceil ={(\lfloor x\rfloor )}^2+2x$$ Commented by rish@bh last updated on 11/Jun/17 $$\mathrm{I}\mathrm{got}\mathrm{only}0\mathrm{and}.5\mathrm{but}\mathrm{my}\mathrm{book}$$$$\mathrm{says}\:\frac{{n}+\mathrm{1}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{0} \…

Question Number 81010 by M±th+et£s last updated on 08/Feb/20 $$showthat$$$${(cos\theta -isin\theta )}^n=(cosn\theta -isin\theta )$$ Commented by MJS last updated on 08/Feb/20 $$\mathrm{wrong}$$…

Question Number 146535 by mathdanisur last updated on 13/Jul/21 $$\{\begin{array}{l}\frac{15}{x^2+xy}+\frac{3}{y^2+xy}=5,5\\ \frac{12}{x^2+xy}-\frac{6}{y^2+xy}=3\end{array}\Rightarrow \mid x+y\mid =?$$ Answered by liberty last updated on 14/Jul/21 $$\:\begin{cases}{\frac{\mathrm{30}}{{x}^{\mathrm{2}} +{xy}}+\frac{\mathrm{6}}{{y}^{\mathrm{2}}…

Question Number 146521 by mathdanisur last updated on 13/Jul/21 $${(\mathit{i}-1)}^{-100}=?$$ Answered by mathmax by abdo last updated on 13/Jul/21 $$\left(\mathrm{i}−\mathrm{1}\right)^{−\mathrm{100}} =\left(−\mathrm{1}+\mathrm{i}\right)^{−\mathrm{100}} \:=\left(\sqrt{\mathrm{2}}\mathrm{e}^{\frac{\mathrm{i3}\pi}{\mathrm{4}}}…

Question Number 146508 by mathdanisur last updated on 13/Jul/21 $$Findthesumoftherootsofthe$$$$equation:$$$$16\cdot 2^{\mid \mathit{x}\mid }+5\cdot 2^{\mathit{x}}=42$$ Answered by Olaf_Thorendsen last updated on 13/Jul/21…