Menu Close

Category: Algebra

Question-122214

Question Number 122214 by peter frank last updated on 14/Nov/20 Answered by floor(10²Eta[1]) last updated on 14/Nov/20 $$\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{has}\:\mathrm{a}\:\mathrm{repeated}\:\mathrm{root}\:\mathrm{so}\:\mathrm{f}'\left(\mathrm{x}\right)\:\mathrm{has}\:\mathrm{that}\:\mathrm{root} \\ $$$$\mathrm{f}'\left(\mathrm{x}\right)=\mathrm{54x}^{\mathrm{2}} +\mathrm{6x}−\mathrm{88}=\mathrm{0}=\mathrm{27x}^{\mathrm{2}} +\mathrm{3x}−\mathrm{44} \\ $$$$\mathrm{x}=\frac{−\mathrm{1}\pm\sqrt{\mathrm{1}+\mathrm{4}.\mathrm{44}.\mathrm{3}}}{\mathrm{18}}=\frac{−\mathrm{1}\pm\mathrm{23}}{\mathrm{18}} \\…

x-5-ax-4-cx-2-dx-e-0-let-x-rt-s-t-p-Find-r-s-p-such-that-equation-gets-transformed-to-t-5-Dt-E-0-

Question Number 56641 by ajfour last updated on 20/Mar/19 $$\mathrm{x}^{\mathrm{5}} +\mathrm{ax}^{\mathrm{4}} +\mathrm{cx}^{\mathrm{2}} +\mathrm{dx}+\mathrm{e}=\mathrm{0} \\ $$$$\mathrm{let}\:\mathrm{x}=\frac{\mathrm{rt}+\mathrm{s}}{\mathrm{t}+\mathrm{p}}\:\:.\:\mathrm{Find}\:\mathrm{r},\mathrm{s},\mathrm{p}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{equation}\:\mathrm{gets}\:\mathrm{transformed} \\ $$$$\mathrm{to}\:\:\:\:\:\lambda\mathrm{t}^{\mathrm{5}} +\mathrm{Dt}+\mathrm{E}=\mathrm{0}. \\ $$ Commented by ajfour…

If-x-5-3-then-x-3-1-x-3-or-is-it-possible-at-all-

Question Number 122174 by AbdullahMohammadNurusSafa last updated on 14/Nov/20 $${If}\:\:\boldsymbol{{x}}\:=\:\sqrt{\mathrm{5}\:}\:+\:\sqrt{\mathrm{3}},{then}\:\boldsymbol{{x}}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\boldsymbol{{x}}^{\mathrm{3}} }\:=\:? \\ $$$$\boldsymbol{{or}},\:\boldsymbol{{is}}\:\boldsymbol{{it}}\:\boldsymbol{{possible}}\:\boldsymbol{{at}}\:\boldsymbol{{all}}? \\ $$ Answered by behi83417@gmail.com last updated on 14/Nov/20 $$\mathrm{x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}}…

Given-that-I-n-0-1-x-1-x-n-dx-obtain-a-reduction-formulae-for-I-n-in-terms-of-I-n-2-Hence-evaluate-0-1-x-1-x-5-dx-

Question Number 122166 by physicstutes last updated on 14/Nov/20 $$\mathrm{Given}\:\mathrm{that}\:{I}_{{n}} \:=\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}\left(\mathrm{1}−{x}\right)^{{n}} {dx} \\ $$$$\mathrm{obtain}\:\mathrm{a}\:\mathrm{reduction}\:\mathrm{formulae}\:\mathrm{for}\:{I}_{{n}\:} \:\mathrm{in}\:\mathrm{terms} \\ $$$$\mathrm{of}\:{I}_{{n}−\mathrm{2}} \:\mathrm{Hence}\:\mathrm{evaluate}\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}\left(\mathrm{1}−{x}\right)^{\mathrm{5}} {dx}. \\ $$…

If-f-x-sin-cos-x-pi-x-f-pi-2-

Question Number 187695 by mnjuly1970 last updated on 20/Feb/23 $$ \\ $$$$\:\:\:{If}\:,\:\:{f}\left(\:{x}\:\right)=\:\frac{\:\:{si}\underset{} {{n}}\:\left({cos}\:\left({x}\right)\:\right)}{\overset{} {\:}\sqrt{\:\frac{\pi}{{x}}}} \\ $$$$\:\:\:\:\Rightarrow\:\:\:{f}\:'\:\left(\frac{\:\pi}{\mathrm{2}}\:\right)\:=\:? \\ $$ Answered by horsebrand11 last updated on 20/Feb/23…

Sum-the-series-sin-2-sin-2-2-sin-2-3-sin-2-n-

Question Number 56602 by Tawa1 last updated on 19/Mar/19 $$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{sin}^{\mathrm{2}} \left(\alpha\right)\:+\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{2}\alpha\right)\:+\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{3}\alpha\right)\:+\:…\:+\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{n}\alpha\right) \\ $$ Commented by maxmathsup by imad last updated…