Question Number 142045 by Engr_Jidda last updated on 25/May/21 Answered by Dwaipayan Shikari last updated on 25/May/21 $${y}=\left(\frac{\mathrm{1}}{{x}}\right)^{{x}} \\ $$$${log}\left({y}\right)=−{xlog}\left({x}\right)\Rightarrow\frac{{y}'}{{y}}=−\mathrm{1}−{log}\left({x}\right)\Rightarrow{y}=−{x}^{−{x}} \left(\mathrm{1}+{log}\left({x}\right)\right) \\ $$ Commented by…
Question Number 142036 by mathsuji last updated on 25/May/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 10970 by Joel576 last updated on 04/Mar/17 $${x}^{{x}^{{x}^{\iddots^{\mathrm{2}} } } } \:=\:\mathrm{2} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:? \\ $$ Answered by ridwan balatif last updated on…
Question Number 142025 by mnjuly1970 last updated on 25/May/21 Answered by som(math1967) last updated on 25/May/21 $$\left(\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{c}}\right)^{\mathrm{2}} =\mathrm{1} \\ $$$$\mathrm{2}\left(\boldsymbol{{ab}}+\boldsymbol{{bc}}+\boldsymbol{{ca}}\right)=\mathrm{1}−\mathrm{2} \\ $$$$\boldsymbol{{ab}}+\boldsymbol{{bc}}+\boldsymbol{{ca}}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\boldsymbol{{a}}^{\mathrm{3}} +\boldsymbol{{b}}^{\mathrm{3}}…
Question Number 10944 by 314159 last updated on 03/Mar/17 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{ordered}\:\mathrm{pairs}\:\left(\mathrm{a},\mathrm{b}\right)\:\mathrm{so}\:\mathrm{that}\:\frac{\mathrm{ab}}{\mathrm{a}+\mathrm{b}}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}. \\ $$$$\left(\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{are}\:\mathrm{integers}\right). \\ $$ Commented by FilupS last updated on 03/Mar/17 $${n}=\frac{{ab}}{{a}+{b}},\:\:\:\:\:{n},\:{a},\:{b}\:\in\:\mathbb{Z} \\ $$$$\: \\…
Question Number 10933 by Joel576 last updated on 02/Mar/17 $$\mathrm{If}\:\:{p}\:\:\mathrm{and}\:\:{q}\:\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{for}\:\mathrm{the} \\ $$$${x}^{\mathrm{2}} \:−\:\left({a}\:+\:\mathrm{1}\right){x}\:+\:\left(−{a}\:−\:\frac{\mathrm{5}}{\mathrm{2}}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{The}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\:{p}^{\mathrm{2}\:} +\:{q}^{\mathrm{2}} \:\:\mathrm{is}\:… \\ $$ Answered by ridwan balatif last updated…
Question Number 10907 by j.masanja06@gmail.com last updated on 01/Mar/17 $$\mathrm{express}\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fraction} \\ $$$$\frac{\mathrm{3x}+\mathrm{2}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{x}+\mathrm{1}\right)} \\ $$ Answered by sandy_suhendra last updated on 01/Mar/17 $$=\frac{\mathrm{3x}+\mathrm{2}}{\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}+\mathrm{1}\right)}=\frac{\mathrm{3x}+\mathrm{2}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}−\mathrm{1}\right)} \\…
Question Number 76438 by john santu last updated on 27/Dec/19 $${given}\:{N}\:=\frac{\mathrm{4}}{\left(\sqrt{\mathrm{5}}+\mathrm{1}\right)\left(\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{4}}} +\mathrm{1}\right)\left(\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{8}}} +\mathrm{1}\right)\left(\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{16}}} +\mathrm{1}\right)} \\ $$$${find}\:{value}\:{of}\:\left({N}+\mathrm{1}\right)^{\mathrm{48}} . \\ $$ Answered by mr W last updated…
Question Number 76436 by Master last updated on 27/Dec/19 Answered by john santu last updated on 27/Dec/19 $$\frac{\mathrm{1}}{{abc}}+\frac{{a}+{c}}{{ac}}=\frac{\mathrm{1}}{{b}} \\ $$$$\frac{{ab}+{bc}+\mathrm{1}}{{abc}}=\frac{\mathrm{1}}{{b}}\rightarrow{ab}+{bc}+\mathrm{1}={ac} \\ $$$${ab}+{bc}={ac}−\mathrm{1}\:\rightarrow{b}=\frac{{ac}−\mathrm{1}}{{a}+{c}} \\ $$$${by}\:{substitusi} \\…
Question Number 76428 by TawaTawa last updated on 27/Dec/19 Answered by john santu last updated on 27/Dec/19 $$\left(\mathrm{5}\right){ratio}\:=\:\frac{{a}_{\mathrm{2}} }{{a}_{\mathrm{1}} }.\:\rightarrow{a}_{\mathrm{2}} =\mathrm{10}.{a}_{\mathrm{1}} =\mathrm{10}. \\ $$$${now}\:{a}_{{n}\:} ={a}_{\mathrm{1}}…