Question Number 21422 by Tinkutara last updated on 23/Sep/17 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{integer}\:\mathrm{values}\:\mathrm{of}\:{a}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{quadratic}\:\mathrm{expression} \\ $$$$\left({x}\:+\:{a}\right)\left({x}\:+\:\mathrm{1991}\right)\:+\:\mathrm{1}\:\mathrm{can}\:\mathrm{be}\:\mathrm{factored} \\ $$$$\mathrm{as}\:\mathrm{a}\:\mathrm{product}\:\left({x}\:+\:{b}\right)\left({x}\:+\:{c}\right)\:\mathrm{where}\:{b}\:\mathrm{and} \\ $$$${c}\:\mathrm{are}\:\mathrm{integers}. \\ $$ Commented by Tikufly last updated…
Question Number 152481 by mathdanisur last updated on 28/Aug/21 Commented by Rasheed.Sindhi last updated on 29/Aug/21 $$\boldsymbol{{Some}}\:{solutions}: \\ $$$$\left({x},{y},{z}\right)=\left(\mathrm{3},\mathrm{3},\mathrm{8}\right),\left(\mathrm{3},\mathrm{8},\mathrm{3}\right),\left(\mathrm{8},\mathrm{3},\mathrm{3}\right) \\ $$ Answered by Rasheed.Sindhi last…
Question Number 152464 by mathdanisur last updated on 28/Aug/21 Answered by mindispower last updated on 29/Aug/21 $$\frac{{sin}\left({z}\right)}{{z}}=\underset{{n}\geqslant\mathrm{1}} {\prod}\left(\mathrm{1}−\frac{{z}^{\mathrm{2}} }{{n}^{\mathrm{2}} \pi^{\mathrm{2}} }\right) \\ $$$$\frac{{sh}\left({t}\right)}{{t}}=\underset{{n}\geqslant\mathrm{1}} {\prod}\left(\mathrm{1}+\frac{{t}^{\mathrm{2}} }{{n}^{\mathrm{2}}…
Question Number 86924 by TawaTawa1 last updated on 01/Apr/20 Answered by mind is power last updated on 01/Apr/20 $$={x}\underset{{n}\geqslant\mathrm{1}} {\sum}.\frac{\left(−\mathrm{2}{x}^{\mathrm{2}} \right)^{{n}} }{{n}^{\mathrm{2}} }={U}_{{n}} \\ $$$$\int\frac{{ln}\left(\mathrm{1}+{x}\right)}{{x}}{dx}=\int\underset{{n}\geqslant\mathrm{0}}…
Question Number 152457 by pete last updated on 28/Aug/21 $$ \\ $$$$\mathrm{Kofi}\:\mathrm{is}\:\mathrm{20\%}\:\:\mathrm{heavier}\:\mathrm{than}\:\mathrm{Afia}.\:\mathrm{If}\:\mathrm{Kofi} \\ $$$$\mathrm{weighs}\:\mathrm{60}\:\mathrm{kg}\:\mathrm{what}\:\mathrm{is}\:\mathrm{Afia}'\mathrm{s}\:\mathrm{weight}? \\ $$ Answered by Rasheed.Sindhi last updated on 28/Aug/21 $${Let}\:{Afia}'{s}\:{weight}\:{is}\:{w} \\…
Question Number 86903 by A8;15: last updated on 01/Apr/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 21355 by Tinkutara last updated on 21/Sep/17 $$\mathrm{Solve}\::\:\mid{x}^{\mathrm{2}} \:+\:\mathrm{3}{x}\mid\:+\:{x}^{\mathrm{2}} \:−\:\mathrm{2}\:\geqslant\:\mathrm{0} \\ $$ Answered by mrW1 last updated on 22/Sep/17 $$\mid\mathrm{x}^{\mathrm{2}} +\mathrm{3x}\mid\geqslant\mathrm{2}−\mathrm{x}^{\mathrm{2}} \\ $$$$…
Question Number 21356 by Tinkutara last updated on 21/Sep/17 $$\mathrm{Solve}\::\:\sqrt[{\mathrm{3}}]{\mathrm{2}^{\frac{\mathrm{3}{x}−\mathrm{1}}{{x}−\mathrm{1}}} }\:<\:\mathrm{8}^{\frac{{x}−\mathrm{3}}{\mathrm{3}{x}−\mathrm{7}}} \\ $$ Answered by dioph last updated on 21/Sep/17 $${x}−\mathrm{1}\:\neq\:\mathrm{0}\:\Rightarrow\:{x}\:\neq\:\mathrm{1} \\ $$$$\mathrm{3}{x}−\mathrm{7}\:\neq\:\mathrm{0}\:\Rightarrow\:{x}\:\neq\:\frac{\mathrm{7}}{\mathrm{3}} \\ $$$$\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{3}}×\frac{\mathrm{3}{x}−\mathrm{1}}{{x}−\mathrm{1}}}…
Question Number 21357 by Tinkutara last updated on 21/Sep/17 $$\mathrm{Solve}\::\:\mathrm{log}_{\mathrm{2}{x}+\mathrm{3}} {x}^{\mathrm{2}} \:<\:\mathrm{1} \\ $$ Answered by dioph last updated on 21/Sep/17 $$\mathrm{2}{x}\:+\:\mathrm{3}\:>\:\mathrm{0}\:\Rightarrow\:{x}\:>\:−\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\mathrm{2}{x}\:+\:\mathrm{3}\:\neq\:\mathrm{1}\:\Rightarrow\:{x}\:\neq\:−\mathrm{1} \\…
Question Number 21354 by Tinkutara last updated on 21/Sep/17 $$\mathrm{Solve}\::\:\sqrt{\mathrm{2}{x}\:+\:\mathrm{5}}\:+\:\sqrt{{x}\:−\:\mathrm{1}}\:>\:\mathrm{8} \\ $$ Commented by Tinkutara last updated on 22/Sep/17 $${Where}\:{is}\:{my}\:{mistake}? \\ $$$$\sqrt{\mathrm{2}{x}+\mathrm{5}}+\sqrt{{x}−\mathrm{1}}>\mathrm{8} \\ $$$$\mathrm{2}{x}+\mathrm{5}+{x}−\mathrm{1}+\mathrm{2}\sqrt{\left(\mathrm{2}{x}+\mathrm{5}\right)\left({x}−\mathrm{1}\right)}>\mathrm{64} \\…