Question Number 163891 by HongKing last updated on 11/Jan/22 $$\mathrm{if}\:\:\:\mathrm{f}\left(\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1}\right)\:=\:\mathrm{x}^{\mathrm{5}} \:+\:\mathrm{4x}\:+\:\mathrm{2} \\ $$$$\mathrm{find}\:\:\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:? \\ $$ Answered by Ar Brandon last updated on…
Question Number 163865 by mathlove last updated on 11/Jan/22 Answered by TheSupreme last updated on 11/Jan/22 $${x}\neq\pm\mathrm{1} \\ $$$$ \\ $$ Commented by mr W…
Question Number 163861 by mathlove last updated on 11/Jan/22 Answered by Ar Brandon last updated on 11/Jan/22 $${x}=\sqrt{\mathrm{5}}+\frac{\mathrm{1}}{{x}}\Rightarrow{x}=\frac{\sqrt{\mathrm{5}}\pm\sqrt{\mathrm{9}}}{\mathrm{2}}=\frac{\sqrt{\mathrm{5}}+\mathrm{3}}{\mathrm{2}}\:\left({x}>\mathrm{0},\:\sqrt{\mathrm{5}}−\mathrm{3}<\mathrm{0}\right) \\ $$ Terms of Service Privacy Policy…
Question Number 163860 by mathlove last updated on 11/Jan/22 Answered by Ar Brandon last updated on 11/Jan/22 $$\Rightarrow\sqrt[{\mathrm{4}}]{{x}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{{x}}}+\sqrt[{\mathrm{4}}]{{x}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{{x}}}=\mathrm{5} \\ $$$$\Rightarrow\mathrm{2}\sqrt[{\mathrm{4}}]{{x}}+\frac{\mathrm{2}}{\:\sqrt[{\mathrm{4}}]{{x}}}=\mathrm{5} \\ $$$$\Rightarrow\mathrm{2}\sqrt[{\mathrm{4}}]{{x}^{\mathrm{2}} }−\mathrm{5}\sqrt[{\mathrm{4}}]{{x}}+\mathrm{2}=\mathrm{0} \\ $$$$\Rightarrow\sqrt[{\mathrm{4}}]{{x}}=\frac{\mathrm{5}\pm\sqrt{\mathrm{9}}}{\mathrm{4}}…
Question Number 32788 by rahul 19 last updated on 02/Apr/18 $$\boldsymbol{{T}}{he}\:{least}\:{positive}\:{integral}\:{value}\:{of} \\ $$$$'{x}'\:{satisfying}\:: \\ $$$$\left({e}^{{x}} −\mathrm{2}\right)\left(\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)\right)\left({x}−\mathrm{log}_{{e}} \:\underset{} {\mathrm{2}}\right)\left({sinx}\:−\:{cosx}\right)<\mathrm{0} \\ $$ Commented by rahul 19 last…
Question Number 163856 by mathlove last updated on 11/Jan/22 Answered by bobhans last updated on 11/Jan/22 $$\:\frac{\mathrm{49}}{\mathrm{15}}\:=\:\mathrm{3}+\frac{\mathrm{4}}{\mathrm{15}}\:=\:\mathrm{3}+\frac{\mathrm{1}}{\left(\frac{\mathrm{15}}{\mathrm{4}}\right)}\:=\:\mathrm{3}+\frac{\mathrm{1}}{\mathrm{3}+\frac{\mathrm{3}}{\mathrm{4}}}\:=\:\mathrm{3}+\frac{\mathrm{1}}{\mathrm{3}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}}} \\ $$$$\:\mathrm{x}=\mathrm{3},\:\mathrm{y}=\mathrm{1}\:,\:\mathrm{z}=\:\mathrm{x}=\mathrm{3}\:\rightarrow\sqrt{\mathrm{xyz}}\:=\:\mathrm{3}=\mathrm{x}=\mathrm{z} \\ $$ Commented by mathlove last…
Question Number 163849 by alephzero last updated on 11/Jan/22 $$\frac{\mathrm{1}}{\mathrm{1}\:\centerdot\:\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{2}\:\centerdot\:\mathrm{3}}\:+\:…\:\frac{\mathrm{1}}{\mathrm{19}\:\centerdot\:\mathrm{20}}\:+\:\frac{\mathrm{1}}{\mathrm{20}\:\centerdot\:\mathrm{21}}\:=\:? \\ $$ Answered by cortano1 last updated on 11/Jan/22 $$\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{20}} {\sum}}\:\frac{\mathrm{1}}{{k}\left({k}+\mathrm{1}\right)}\:=\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{20}} {\sum}}\:\left(\frac{\mathrm{1}}{{k}}−\frac{\mathrm{1}}{{k}+\mathrm{1}}\right) \\…
Question Number 32780 by fara1990 last updated on 02/Apr/18 $$\mathrm{10}−\mathrm{8}=\frac{{p}}{\mathrm{9}} \\ $$ Answered by Rio Mike last updated on 02/Apr/18 $$\mathrm{2}\:=\:\frac{{p}}{\mathrm{9}} \\ $$$${p}=\mathrm{2}×\mathrm{9} \\ $$$$\mathrm{p}=\mathrm{18}…
Question Number 163845 by mnjuly1970 last updated on 12/Jan/22 $$ \\ $$$$\:\:\:\:\:\:\:{a},\:{b}\:\in\:\mathbb{N}\:\:,\:\:{gcd}\left(\:{a}\:,\:\:{b}\:\right)=\mathrm{1} \\ $$$$\:\:\:\:\:{prove}\:\:{that}\: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{a}^{\:\:\varphi\:\left({b}\:\right)} +\:{b}^{\:\varphi\:\left({a}\:\right)} \:\overset{\:{ab}} {\equiv}\:\mathrm{1} \\ $$$$\:\:\:\:\:\varphi\::\:\:\:\mathscr{E}{uler}\:{phi}\:\:{function}\:… \\ $$$$…
Question Number 163844 by HongKing last updated on 11/Jan/22 Terms of Service Privacy Policy Contact: info@tinkutara.com