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}} \\ $$$${p}=\mathrm{2}×\mathrm{9} \\ $$$$\mathrm{p}=\mathrm{18}…
Question Number 163845 by mnjuly1970 last updated on 12/Jan/22 $$ \\ $$$$\:\:\:\:\:\:\:{a},\:{b}\:\in\:\mathbb{N}\:\:,\:\:{gcd}\left(\:{a}\:,\:\:{b}\:\right)=\mathrm{1} \\ $$$$\:\:\:\:\:{prove}\:\:{that}\: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{a}^{\:\:\varphi\:\left({b}\:\right)} +\:{b}^{\:\varphi\:\left({a}\:\right)} \:\overset{\:{ab}} {\equiv}\:\mathrm{1} \\ $$$$\:\:\:\:\:\varphi\::\:\:\:\mathscr{E}{uler}\:{phi}\:\:{function}\:… \\ $$$$…
Question Number 163844 by HongKing last updated on 11/Jan/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163843 by HongKing last updated on 11/Jan/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32767 by Rasheed.Sindhi last updated on 01/Apr/18 $$\mathrm{For}\:{a},{b},{c}\geqslant\mathrm{0}\:\mathrm{if}\:{a}+{b}+{c}={n},\:\mathrm{determine} \\ $$$$\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum}\:\mathrm{values}\:\mathrm{of} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{ab}−{bc}−{ca}. \\ $$ Commented by Rasheed.Sindhi last updated on…
Question Number 32768 by Rasheed.Sindhi last updated on 01/Apr/18 $$\mathrm{Prove}\:\mathrm{that}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} \geqslant{ab}+{bc}+{ca} \\ $$$$\forall\:{a},{b},{c}\in\mathbb{R} \\ $$ Answered by mrW2 last updated on 02/Apr/18 $${a}^{\mathrm{2}}…
Question Number 163833 by mathlove last updated on 11/Jan/22 Commented by mr W last updated on 11/Jan/22 $${x}=\overset{\sim} {\boldsymbol{\mathcal{W}}}\left(\mathrm{36}\right)\approx\mathrm{2}.\mathrm{107036463957} \\ $$ Commented by Tawa11 last…
Question Number 98293 by I want to learn more last updated on 12/Jun/20 Answered by mr W last updated on 12/Jun/20 $${see}\:{Q}\mathrm{97675} \\ $$$${x}+{y}+{z}=\mathrm{0} \\…