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Author: Tinku Tara

x-1-x-3-dx-

Question Number 152660 by Tawa11 last updated on 30/Aug/21 $$\int\:\frac{\mathrm{x}}{\:\sqrt{\mathrm{1}\:\:\:+\:\:\:\mathrm{x}^{\mathrm{3}} }}\:\mathrm{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 31/Aug/21 $$\left(\mathrm{1}+{u}\right)^{−\frac{\mathrm{1}}{\mathrm{2}}} \:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \frac{\left(\mathrm{2}{n}\right)!}{\mathrm{2}^{\mathrm{2}{n}}…

If-x-3-x-3-0-has-the-roots-a-b-and-c-determine-the-monic-polynomial-with-the-roots-a-5-b-5-and-c-5-Q152396-

Question Number 152663 by mr W last updated on 31/Aug/21 $$\mathrm{If}\:\:\mathrm{x}^{\mathrm{3}} -\mathrm{x}+\mathrm{3}=\mathrm{0}\:\mathrm{has}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{a},\:\mathrm{b}\:\mathrm{and}\:\mathrm{c}. \\ $$$$\mathrm{determine}\:\mathrm{the}\:\mathrm{monic}\:\mathrm{polynomial}\:\mathrm{with} \\ $$$$\mathrm{the}\:\mathrm{roots}\:\:\mathrm{a}^{\mathrm{5}} ,\:\mathrm{b}^{\mathrm{5}} \:\mathrm{and}\:\:\mathrm{c}^{\mathrm{5}} . \\ $$$$\left[{Q}\mathrm{152396}\right] \\ $$ Answered by…

Show-that-if-G-is-a-finite-group-of-even-order-then-G-has-an-odd-number-of-elements-of-order-2-

Question Number 21588 by dioph last updated on 28/Sep/17 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{if}\:{G}\:\mathrm{is}\:\mathrm{a}\:\mathrm{finite}\:\mathrm{group}\:\mathrm{of} \\ $$$$\mathrm{even}\:\mathrm{order},\:\mathrm{then}\:{G}\:\mathrm{has}\:\mathrm{an}\:\mathrm{odd} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{elements}\:\mathrm{of}\:\mathrm{order}\:\mathrm{2}. \\ $$ Commented by arcana last updated on 02/Dec/18 $$\mathrm{los}\:\mathrm{elementos}\:\mathrm{son}\:\mathrm{subgrupos}\:\mathrm{de}\:\mathrm{G}? \\…

If-n-objects-are-arranged-in-a-row-then-find-the-number-of-ways-of-selecting-three-of-these-objects-so-that-no-two-of-them-are-next-to-each-other-

Question Number 21587 by Tinkutara last updated on 28/Sep/17 $$\mathrm{If}\:{n}\:\mathrm{objects}\:\mathrm{are}\:\mathrm{arranged}\:\mathrm{in}\:\mathrm{a}\:\mathrm{row},\:\mathrm{then} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{of}\:\mathrm{selecting} \\ $$$$\mathrm{three}\:\mathrm{of}\:\mathrm{these}\:\mathrm{objects}\:\mathrm{so}\:\mathrm{that}\:\mathrm{no}\:\mathrm{two}\:\mathrm{of} \\ $$$$\mathrm{them}\:\mathrm{are}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}. \\ $$ Commented by mrW1 last updated on 29/Sep/17…