Question Number 222225 by mathBagja last updated on 21/Jun/25 $${a}+{b}+{c}=−{D} \\ $$$${ab}+{bc}+{ac}={E} \\ $$$${abc}=−\mathrm{1} \\ $$$$\left({a}^{\mathrm{2}} −{bc}\right)\left({b}^{\mathrm{2}} −{ac}\right)\left({c}^{\mathrm{2}} −{ab}\right)=\mathrm{40} \\ $$$${D}−{E}=\mathrm{4} \\ $$$$\left({D}+{E}\right)^{\mathrm{2}} =… \\…
Question Number 222172 by hardmath last updated on 19/Jun/25 $$\frac{\mathrm{4}}{\mathrm{5}}\:>\:\frac{\mathrm{8}}{\mathrm{3x}\:−\:\mathrm{6}}\:>\:\frac{\mathrm{2}}{\mathrm{9}} \\ $$$$\mathrm{find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by A5T last updated on 19/Jun/25 $$\frac{\mathrm{4}}{\mathrm{5}}>\frac{\mathrm{8}}{\mathrm{3x}−\mathrm{6}}\:\mathrm{and}\:\mathrm{3x}−\mathrm{6}>\mathrm{0}\:\left(\mathrm{x}>\mathrm{2}\right)\Rightarrow\:\mathrm{12x}−\mathrm{24}>\mathrm{40} \\ $$$$\Rightarrow\mathrm{x}>\frac{\mathrm{16}}{\mathrm{3}}\:…\:\left(\mathrm{i}\right) \\…
Question Number 222141 by fantastic last updated on 19/Jun/25 $${x}^{\mathrm{2}} +\left(\frac{{x}}{\mathrm{2}{x}−\mathrm{1}}\right)^{\mathrm{2}} =\mathrm{12} \\ $$ Answered by Rasheed.Sindhi last updated on 19/Jun/25 $${x}^{\mathrm{2}} \left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{2}} −\mathrm{12}\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{2}} +{x}^{\mathrm{2}}…
Question Number 222184 by hardmath last updated on 19/Jun/25 $$\mathrm{f}\left(\mathrm{2}\right)\:=\:\mathrm{8} \\ $$$$\mathrm{f}\left(\mathrm{3}\right)\:=\:\mathrm{5} \\ $$$$\int_{\mathrm{2}} ^{\:\mathrm{3}} \:\left(\mathrm{f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\:^{'} \left(\mathrm{x}\right)\centerdot\mathrm{x}\right)\:\mathrm{dx}\:=\:? \\ $$ Answered by wewji12 last updated on…
Question Number 222125 by hardmath last updated on 18/Jun/25 $$\mathrm{If}:\:\:\:\mathrm{log}_{\mathrm{3}} \left(\mathrm{5}^{\boldsymbol{\mathrm{x}}} \:+\:\frac{\mathrm{1}}{\mathrm{5}^{\boldsymbol{\mathrm{x}}} }\:+\:\mathrm{7}\right)\:\:\:\Rightarrow\:\:\:\mathrm{min}\:=\:? \\ $$ Commented by mr W last updated on 18/Jun/25 $${you}\:{mean} \\…
Question Number 222076 by Tawa11 last updated on 16/Jun/25 Answered by Ghisom last updated on 17/Jun/25 $$\mathrm{different}\:\mathrm{methods},\:\mathrm{I}\:\mathrm{like}\:\mathrm{this}\:\mathrm{one}: \\ $$$${x}={I}+{f};\:{I}\in\mathbb{Z}\wedge{f}\in\mathbb{R}\wedge\mathrm{0}\leqslant{f}<\mathrm{1} \\ $$$$\mathrm{4}\left({I}+{f}\right)^{\mathrm{2}} −\mathrm{40}{I}+\mathrm{51}=\mathrm{0} \\ $$$$\mathrm{solving}\:\mathrm{for}\:{f}: \\…
Question Number 222066 by MathematicalUser2357 last updated on 16/Jun/25 Commented by fantastic last updated on 16/Jun/25 $${Q}.\mathrm{222001} \\ $$ Commented by MathematicalUser2357 last updated on…
Question Number 222031 by fantastic last updated on 15/Jun/25 $${x}^{{x}} =−\mathrm{1} \\ $$$${Number}\:{of}\:{solutions}?? \\ $$ Answered by mr W last updated on 15/Jun/25 $${solve}\:\boldsymbol{{z}}^{\boldsymbol{{z}}} =−\mathrm{1}{for}\:\boldsymbol{{z}}\in\boldsymbol{{C}}.…
Question Number 222026 by fantastic last updated on 15/Jun/25 $${If}\:\left(\mathrm{1}.\mathrm{234}\right)^{{a}} =\left(\mathrm{0}.\mathrm{1234}\right)^{{b}} =\mathrm{10}^{{c}} \\ $$$${prove}\:{that}\:\frac{\mathrm{1}}{{a}}−\frac{\mathrm{1}}{{c}}=\frac{\mathrm{1}}{{b}} \\ $$ Answered by som(math1967) last updated on 15/Jun/25 $$\left(\mathrm{1}.\mathrm{234}\right)^{{a}} =\left(\mathrm{0}.\mathrm{1234}\right)^{{b}}…
Question Number 221968 by MathematicalUser2357 last updated on 14/Jun/25 $$\left({a}+{b}+{c}\right)^{\mathrm{3}} \\ $$ Answered by MrGaster last updated on 14/Jun/25 Commented by MathematicalUser2357 last updated on…