Question Number 156063 by cortano last updated on 07/Oct/21 $$\:\:\:\:\frac{\mathrm{2}}{\mathrm{x}}+\frac{\mathrm{3}}{\mathrm{x}+\mathrm{1}}+\frac{\mathrm{4}}{\mathrm{x}+\mathrm{2}}+\frac{\mathrm{5}}{\mathrm{x}+\mathrm{3}}+\frac{\mathrm{6}}{\mathrm{x}+\mathrm{4}}=\mathrm{5} \\ $$ Commented by john_santu last updated on 07/Oct/21 $${x}=\left\{\mathrm{2},\:−\mathrm{2}\pm\:\sqrt{\frac{\mathrm{15}\pm\sqrt{\mathrm{145}}}{\mathrm{10}}}\:\right\} \\ $$ Commented by Tawa11…
Question Number 156049 by MathSh last updated on 07/Oct/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 90483 by M±th+et£s last updated on 23/Apr/20 $${prove}\:{that}/\:\frac{{sin}^{\mathrm{3}} {a}}{{sin}\:{b}}+\frac{{cos}^{\mathrm{3}} {a}}{{cos}\:{b}}\geqslant{sec}\left({a}−{b}\right) \\ $$$${for}\:{all}\:{a},{b}\in\:\left(\mathrm{0},\frac{\pi}{\mathrm{2}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 90473 by I want to learn more last updated on 23/Apr/20 Commented by MJS last updated on 24/Apr/20 you want to learn more. I want to know if you have got any idea what a "proper ideal" might be. Commented by I want…
Question Number 155991 by cortano last updated on 07/Oct/21 $$\:\begin{cases}{\mathrm{a}\left(\mathrm{x}+\mathrm{2}\right)+\mathrm{y}=\mathrm{3a}}\\{\mathrm{a}+\mathrm{2x}^{\mathrm{3}} =\mathrm{y}^{\mathrm{3}} +\left(\mathrm{a}+\mathrm{2}\right)\mathrm{x}^{\mathrm{3}} }\end{cases} \\ $$$$\:\mathrm{solve}\:\mathrm{for}\:\mathrm{x}\:\&\mathrm{y}\:\mathrm{in}\:\mathrm{term}\:\mathrm{a} \\ $$ Commented by Rasheed.Sindhi last updated on 07/Oct/21 $${Mr}\:{cortano},\:{if}\:{you}\:{want}\:{answer}…
Question Number 24908 by Tinkutara last updated on 28/Nov/17 $$\mathrm{If}\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{prove} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{inequality}: \\ $$$$\frac{{a}}{{c}\:+\:{a}\:−\:{b}}\:+\:\frac{{b}}{{a}\:+\:{b}\:−\:{c}}\:+\:\frac{{c}}{{b}\:+\:{c}\:−\:{a}}\:\geqslant\:\mathrm{3}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155977 by MathSh last updated on 06/Oct/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155979 by mnjuly1970 last updated on 06/Oct/21 $$ \\ $$$${prove}\:{that}: \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\sqrt{{x}}\:+\sqrt{{y}}}{\left(\mathrm{1}−{xy}\right)\sqrt[{\mathrm{4}}]{{xy}}}\:{dxdy}=\mathrm{4}\:\left(\mathrm{4}\:−\pi\right) \\ $$$$ \\ $$ Terms of Service…
Question Number 155978 by mnjuly1970 last updated on 06/Oct/21 Commented by mr W last updated on 06/Oct/21 $${i}\:{think}\:{for}\:{any}\:{a}\:{the}\:{eqn}.\:{has}\:{always} \\ $$$${solution}. \\ $$ Commented by mr…
Question Number 155969 by mathlove last updated on 06/Oct/21 Answered by MJS_new last updated on 06/Oct/21 $${a}=\sqrt[{\mathrm{2014}}]{\mathrm{2}^{\mathrm{0}} }+\sqrt[{\mathrm{2014}}]{\mathrm{2}^{\mathrm{1}} }+…+\sqrt[{\mathrm{2014}}]{\mathrm{2}^{\mathrm{2013}} }= \\ $$$$=\underset{{n}=\mathrm{0}} {\overset{\mathrm{2013}} {\sum}}\mathrm{2}^{\frac{{n}}{\mathrm{2014}}} \\…