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Category: Algebra

f-x-f-1-1-x-3-1-3-x-3-is-given-find-the-value-of-f-1-

Question Number 177530 by mnjuly1970 last updated on 06/Oct/22 $$ \\ $$$${f}\:\left({x}\:\right)\:+\:{f}\:\left(\frac{\:\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}\:−{x}^{\:\mathrm{3}} }}\:\right)=\:{x}^{\:\mathrm{3}} \\ $$$$\:\:\:\:\:\:{is}\:{given}.\:{find}\:{the}\:{value}\:{of}: \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:{f}\:\left(−\mathrm{1}\right)=? \\ $$$$ \\ $$ Answered by…

Question-111982

Question Number 111982 by houssam last updated on 05/Sep/20 Answered by aleks041103 last updated on 05/Sep/20 $$\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}{a}^{{k}} =\frac{\mathrm{1}}{\mathrm{1}−{a}},\:{for}\:\mid{a}\mid<\mathrm{1} \\ $$$${But}\:{here}\:{a}={i},\:{for}\:{which}\:\mid{a}\mid=\mid{i}\mid=\mathrm{1},\:{which} \\ $$$${means}\:{that}\:{the}\:{sum}\:{doesn}'{t}\:{converge} \\…

Question-177510

Question Number 177510 by Spillover last updated on 06/Oct/22 Commented by mr W last updated on 06/Oct/22 $${sir}:\:{here}\:{is}\:{a}\:{forum},\:{a}\:{public}\:{place} \\ $$$${for}\:{exchanging}\:{with}\:{other}\:{people}.\: \\ $$$${here}\:{you}\:{can}\:{post}\:{your}\:{questions} \\ $$$${to}\:{ask}\:{other}\:{prople}\:{for}\:{solutions}\:{or} \\…

let-p-x-x-i-n-x-i-n-with-i-2-1-1-find-p-x-at-form-a-k-x-k-2-find-the-roots-of-p-x-3-factorize-inside-C-x-p-x-4-factorize-inside-R-x-the-polynom-p-x-5-decompose-the-fraction-F-

Question Number 46425 by maxmathsup by imad last updated on 25/Oct/18 $${let}\:{p}\left({x}\right)=\left({x}+{i}\right)^{{n}} −\left({x}−{i}\right)^{{n}} \:\:\:{with}\:{i}^{\mathrm{2}} =−\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{p}\left({x}\right)\:{at}\:{form}\:\Sigma\:{a}_{{k}} {x}^{{k}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{factorize}\:{inside}\:{C}\left[{x}\right]\:{p}\left({x}\right) \\ $$$$\left.\mathrm{4}\right)\:{factorize}\:{inside}\:{R}\left[{x}\right]\:{the}\:{polynom}\:{p}\left({x}\right) \\…

If-0-lt-a-b-then-a-b-a-b-dx-dy-xy-x-y-b-a-2-log-b-a-log-2-b-a-

Question Number 177492 by Shrinava last updated on 06/Oct/22 $$\mathrm{If}\:\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}\:\:\:\mathrm{then}: \\ $$$$\int_{\:\boldsymbol{\mathrm{a}}} ^{\:\boldsymbol{\mathrm{b}}} \:\int_{\:\boldsymbol{\mathrm{a}}} ^{\:\boldsymbol{\mathrm{b}}} \:\:\frac{\mathrm{dx}\:\mathrm{dy}}{\:\sqrt{\mathrm{xy}\:\left(\mathrm{x}\:+\:\mathrm{y}\right)}}\:\:\leqslant\:\:\frac{\mathrm{b}−\mathrm{a}}{\mathrm{2}}\:\centerdot\:\mathrm{log}\:\left(\frac{\mathrm{b}}{\mathrm{a}}\right)\:+\:\mathrm{log}^{\mathrm{2}} \:\left(\frac{\mathrm{b}}{\mathrm{a}}\right) \\ $$ Terms of Service Privacy Policy Contact:…

let-p-x-1-ix-5-1-with-i-2-1-1-solve-inside-C-x-the-equation-p-x-0-2-factorize-inside-C-x-the-polynom-p-x-

Question Number 46420 by maxmathsup by imad last updated on 25/Oct/18 $${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{ix}\right)^{\mathrm{5}} −\mathrm{1}\:\:{with}\:{i}^{\mathrm{2}} =−\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{solve}\:{inside}\:{C}\left[{x}\right]\:{the}\:{equation}\:{p}\left({x}\right)=\mathrm{0} \\ $$$$\left.\mathrm{2}\right){factorize}\:{inside}\:{C}\left[{x}\right]\:{the}\:{polynom}\:{p}\left({x}\right) \\ $$$$ \\ $$$$ \\ $$ Terms…