Category: Algebra

Question Number 60980 by Tawa1 last updated on 28/May/19 $$\mathrm{Solve}\mathrm{for}\mathrm{x},\mathrm{y},\mathrm{z}$$$$\mathrm{x}(\mathrm{y}+\mathrm{z})=33\dots ..\left(\mathrm{i}\right)$$$$\mathrm{y}(\mathrm{z}+\mathrm{x})=35\dots ..\left(\mathrm{ii}\right)$$$$\mathrm{z}(\mathrm{x}+\mathrm{y})=14\dots ..\left(\mathrm{iii}\right)$$ Commented by Prithwish sen last updated on…

Question Number 192039 by universe last updated on 06/May/23 $$\mathrm{let}x,y,z\mathrm{be}\mathrm{positive}\mathrm{real}\mathrm{number}\mathrm{such}\mathrm{that}$$$$x^4+y^4+z^4=1\mathrm{find}\mathrm{the}\mathrm{minimum}\mathrm{value}$$$$\mathrm{of}$$$$\:\:\:\:\frac{{x}^{\mathrm{3}} }{\mathrm{1}−{x}^{\mathrm{8}} }\:+\:\frac{{y}^{\mathrm{3}} }{\mathrm{1}−{y}^{\mathrm{8}} }\:+\:\frac{{z}^{\mathrm{3}} }{\mathrm{1}−{z}^{\mathrm{8}} }…

Question Number 60946 by Tawa1 last updated on 27/May/19 $$\mathrm{Find}\mathrm{x}:{\mathrm{x}}^{\mathrm{x}}=2\mathrm{x}$$ Commented by Prithwish sen last updated on 27/May/19 $$\mathrm{x}=2$$ Commented…

Question Number 192009 by universe last updated on 05/May/23 $$ifa>1,show$$$$\frac{\underset{k=1}{\sum ^{a^2-1}}\sqrt{a+\sqrt{k}}}{\underset{k=1}{\sum ^{a^2-1}}\sqrt{a-\sqrt{k}}}=\sqrt{2}+1$$ Answered by Skabetix last updated…

Question Number 60905 by necx1 last updated on 27/May/19 $$ifx+\frac{1}{x}=\sqrt{3}.find$$$$x^{24}+x^{18}+x^6+1$$ Answered by ajfour last updated on 27/May/19 $${E}={x}^{\mathrm{24}}…