Question Number 158455 by mnjuly1970 last updated on 04/Nov/21 Answered by MJS_new last updated on 05/Nov/21 $$\sqrt{{x}\lfloor{x}\rfloor+{x}^{\mathrm{2}} \lfloor{x}−\mathrm{1}\rfloor}=\sqrt{{x}\left(\left({x}+\mathrm{1}\right)\lfloor{x}\rfloor−{x}\right)} \\ $$$${g}\left({x}\right)={x}\left(\left({x}+\mathrm{1}\right)\lfloor{x}\rfloor−{x}\right)=\mathrm{0}\:\Leftrightarrow\:{x}=\mathrm{0}\vee\left({x}+\mathrm{1}\right)\lfloor{x}\rfloor={x} \\ $$$$\Rightarrow\:{x}=\mathrm{0}\vee{x}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{but}\:\left(\underset{{x}\rightarrow\mathrm{1}^{−} }…
Question Number 27376 by macanudo last updated on 05/Jan/18 Commented by prakash jain last updated on 05/Jan/18 $$\mathrm{S}=\underset{{k}=\mathrm{0}} {\overset{\mathrm{2}{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} {x}^{{k}} \\ $$$${S}=\mathrm{1}−{x}+{x}^{\mathrm{2}} −{x}^{\mathrm{3}} +{x}^{\mathrm{4}}…
Question Number 158444 by HongKing last updated on 04/Nov/21 $$\mathrm{if}\:\:\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}}\:\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{with} \\ $$$$\frac{\mathrm{2010}}{\mathrm{2011}}\:<\:\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{y}}}\:<\:\frac{\mathrm{2011}}{\mathrm{2012}}\:\:\mathrm{then}\:\mathrm{compute}\:\mathrm{the} \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{for}\:\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\:\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{values}\:\mathrm{of}\:\:\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}}\:\:\mathrm{which}\:\mathrm{achieves} \\ $$$$\mathrm{this}\:\mathrm{minimum} \\ $$ Commented by mr W last…
Question Number 158443 by HongKing last updated on 04/Nov/21 $$\mathrm{How}\:\mathrm{many}\:\mathrm{divisors}\:\mathrm{has}\:\mathrm{the}\:\mathrm{positive} \\ $$$$\mathrm{integer}\:\:\boldsymbol{\mathrm{n}}\:\:\mathrm{which}\:\mathrm{verify} \\ $$$$\mathrm{n}^{\boldsymbol{\mathrm{n}}} \:=\:\mathrm{2027}^{\mathrm{2027}^{\mathrm{2028}} } \:? \\ $$ Answered by MJS_new last updated on…
Question Number 158438 by amin96 last updated on 04/Nov/21 Commented by amin96 last updated on 04/Nov/21 $$ \\ $$ Given the values of x and…
Question Number 92899 by gonzo last updated on 09/May/20 $${y}=−\mathrm{2}.\mathrm{241}{x}+\mathrm{1}.\mathrm{585} \\ $$$${how}\:{do}\:{i}\:{find}\:{value}\:{of}\:{x}\:{by}\:{rearranging} \\ $$ Commented by mr W last updated on 09/May/20 $${x}=\frac{\mathrm{1}.\mathrm{585}−{y}}{\mathrm{2}.\mathrm{241}} \\ $$…
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Question Number 158424 by HongKing last updated on 04/Nov/21 Answered by ghimisi last updated on 04/Nov/21 $${x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} +\mathrm{3}\sqrt[{\mathrm{3}}]{{x}}+\mathrm{3}\sqrt[{\mathrm{3}}]{{y}}+\mathrm{3}\sqrt[{\mathrm{3}}]{{z}}\:\overset{{am}−{gm}} {\geqslant}\mathrm{12}\sqrt[{\mathrm{12}}]{\mathrm{4}{x}^{\mathrm{4}} {y}^{\mathrm{4}} {z}^{\mathrm{4}} }=\mathrm{12}\Rightarrow \\…
Question Number 92885 by unknown last updated on 09/May/20 Commented by unknown last updated on 09/May/20 $${a}+{b}+{c}=\mathrm{3}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:{A} \\ $$ Commented by mr W last updated…
Question Number 92880 by fath035990 last updated on 09/May/20 $$\mathrm{solve}\:\mathrm{8}\varkappa+\mathrm{4}=\mathrm{3}\left(\varkappa−\mathrm{1}\right)+\mathrm{7} \\ $$ Answered by niroj last updated on 09/May/20 $$\:\:\:\mathrm{8}\varkappa+\mathrm{4}=\mathrm{3}\left(\varkappa−\mathrm{1}\right)+\mathrm{7} \\ $$$$\:\:\mathrm{or},\:\mathrm{8}\varkappa+\mathrm{4}=\mathrm{3}\varkappa−\mathrm{3}+\mathrm{7} \\ $$$$\:\:\mathrm{or},\:\:\mathrm{8}\varkappa−\mathrm{3}\varkappa=\:\mathrm{4}−\mathrm{4}\:\:\: \\…