Category: Algebra

Question Number 149636 by SLVR last updated on 06/Aug/21 Answered by mr W last updated on 06/Aug/21 $${Q}\mathrm{1} \\ $$$${x}\:{is}\:{integer},\:{then}\:{x}^{\mathrm{2}} \:{also}\:{integer}. \\ $$$$\left[{x}^{\mathrm{2}} \right]={x}^{\mathrm{2}} ={x}+\mathrm{1}\:{which}\:{has}\:{no}\:{solution}.…

Question Number 149621 by mathdanisur last updated on 06/Aug/21 $$\mathrm{if}\:\:\:\mathrm{2}^{\boldsymbol{{x}}} =\mathrm{3}^{\boldsymbol{{y}}} =\mathrm{7}^{\boldsymbol{{z}}} =\sqrt[{\mathrm{3}}]{\mathrm{42}} \\ $$$$\mathrm{find}\:\:\:\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}+\frac{\mathrm{1}}{{z}}=? \\ $$ Answered by iloveisrael last updated on 06/Aug/21 $$\:\mathrm{If}\:\mathrm{2}^{\mathrm{x}}…

Question Number 149585 by mathdanisur last updated on 06/Aug/21 $${if}\:\:{x};{y};{z}>\mathrm{0}\:\:{and}\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{3}\:\:{then}: \\ $$$$\Sigma\:\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{\left(\mathrm{2}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\left({y}^{\mathrm{2}} +\mathrm{2}{x}^{\mathrm{2}} \right)}\:\geqslant\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$ Answered by…

Question Number 84047 by jagoll last updated on 09/Mar/20 $$\mathrm{how}\:\mathrm{many}\: \\ $$$$\mathrm{natural}\:\mathrm{solution}\:\mathrm{are}\:\mathrm{there}\:\mathrm{for}\: \\ $$$${x}^{\mathrm{2}} \:−\:{y}\:!\:=\:\mathrm{2019}\:. \\ $$ Answered by naka3546 last updated on 09/Mar/20 $$\mathrm{1},\:{sir}\:\:{namely}\:\:\left({x},\:{y}\right)\:=\:\left(\mathrm{45},\:\mathrm{3}\right)…

Question Number 149568 by mathdanisur last updated on 06/Aug/21 $${solve}\:{the}\:{equation}: \\ $$$$\mathrm{20}{z}\left[{z}\right]\:-\:\mathrm{21}\left\{{z}\right\}\:=\:\mathrm{2021} \\ $$$${where}\:\left\{\ast\right\}\:{is}\:{GIF}\:\:{and}\:\:\left\{{z}\right\}\:=\:{z}\:-\:\left[{z}\right] \\ $$ Answered by Olaf_Thorendsen last updated on 06/Aug/21 $$\mathrm{20}{z}\left[{z}\right]−\mathrm{21}\left\{{z}\right\}\:=\:\mathrm{2021}\:\:\:\:\left(\mathrm{1}\right) \\…