Category: Algebra

Question Number 157871 by HongKing last updated on 29/Oct/21 $$\mathrm{if}\mathrm{x};\mathrm{y}>0\mathrm{then}\mathrm{prove}\mathrm{that}:$$$$\frac{\mathrm{x}}{{\mathrm{x}}^2-\mathrm{x}+1}+\frac{\mathrm{y}}{{\mathrm{y}}^2-\mathrm{y}+1}+\frac{\mathrm{xy}}{{\mathrm{x}}^2{\mathrm{y}}^2-\mathrm{xy}+1}⩽$$$$\leqslant\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} -\mathrm{x}+\mathrm{1}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{y}^{\mathrm{2}} -\mathrm{y}+\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} -\mathrm{xy}+\mathrm{1}} \…

Question Number 92324 by I want to learn more last updated on 06/May/20 $$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{x}\mathrm{for}\mathrm{which}\underset{\mathrm{n}=0}{\sum ^{\mathrm{n}=\mathrm{\infty }}}16{(\frac{3}{4}\mathrm{x}+1)}^{\mathrm{n}}$$$$\left(\mathrm{a}\right)\mathrm{Is}\mathrm{convergent}$$$$\left(\mathrm{b}\right)\mathrm{Is}\mathrm{equal}\mathrm{to}10\frac{2}{3}$$ Answered by mr…

Question Number 157851 by emanuelMcCarthy last updated on 28/Oct/21 Commented by otchereabdullai@gmail.com last updated on 29/Oct/21 $$22)\mathrm{Let}\mathrm{g}\left(\mathrm{x}\right)=-{2\mathrm{x}}^3-{3\mathrm{x}}^2+13\mathrm{bx}+20$$$$\mathrm{x}+\mathrm{a}=0\Rightarrow \mathrm{x}=-\mathrm{a}$$$$\mathrm{so}\mathrm{f}(-\mathrm{a})=-56$$$$−\mathrm{2}\left(−\mathrm{a}\right)^{\mathrm{3}}…

Question Number 157839 by gsk2684 last updated on 28/Oct/21 $$findthelastfourdigitsof$$$${11}^{15999}?$$ Answered by Rasheed.Sindhi last updated on 29/Oct/21 $$\mathrm{11}^{\mathrm{15999}} \equiv{x}\left({mod}\:\mathrm{10}^{\mathrm{4}} \right)…

Question Number 157832 by mathlove last updated on 28/Oct/21 Answered by mr W last updated on 28/Oct/21 $$x^{x^{\frac{3}{2}}}=x^x{x}^{\frac{x}{2}}$$$${x}^{{x}^{\frac{\mathrm{3}}{\mathrm{2}}} −\frac{\mathrm{3}{x}}{\mathrm{2}}} =\mathrm{1}…