Question Number 30579 by abdo imad last updated on 23/Feb/18 $${decompose}\:{inside}\:{C}\left[{x}\right]\:{F}=\:\frac{{x}^{{n}} −\mathrm{1}}{{x}^{\mathrm{2}{n}} −\mathrm{1}}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30576 by abdo imad last updated on 23/Feb/18 $${let}\:{consider}\:{the}\:{equation}\:{x}^{\mathrm{3}} \:+{px}\:+{q}\: \\ $$$${find}\:{S}=\:\sum_{{i}\neq{j}} \:\frac{{x}_{{i}} }{{x}_{{j}} }\:. \\ $$ Commented by abdo imad last updated…
Question Number 30578 by abdo imad last updated on 23/Feb/18 $${decompose}\:{F}\left({x}\right)=\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{{n}} }\:{on}\:{C}\left[{x}\right].{with}\:{n}\:{fromN}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30571 by abdo imad last updated on 23/Feb/18 $${decompose}\:{F}\left({x}\right)=\:\frac{\mathrm{1}}{\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right)^{{n}} }\:{on}\:{C}\left[{x}\right]. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 161629 by HongKing last updated on 20/Dec/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30540 by tawa tawa last updated on 23/Feb/18 $$\mathrm{Show}\:\mathrm{that}\:\:\begin{vmatrix}{\mathrm{bc}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{ca}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{ab}}\\{\:\mathrm{a}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{b}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}}\\{\:\mathrm{a}^{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:} \:\mathrm{b}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}^{\mathrm{2}} }\end{vmatrix}\:\:=\:\:\left(\mathrm{b}\:−\:\mathrm{a}\right)\left(\mathrm{c}\:−\:\mathrm{a}\right)\left(\mathrm{c}\:−\:\mathrm{b}\right)\left(\mathrm{ab}\:+\:\mathrm{bc}\:+\:\mathrm{ac}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30541 by awi123 last updated on 23/Feb/18 $$\mathrm{4}{n}\mathrm{568} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 96072 by i jagooll last updated on 29/May/20 $$\left(\mathrm{x}^{\mathrm{2}} +\mathrm{24x}+\mathrm{24}\right).\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{24}\right)=\:\mathrm{24x}^{\mathrm{2}} \\ $$ Answered by bobhans last updated on 29/May/20 $$\mathrm{set}\:\mathrm{x}^{\mathrm{2}} +\mathrm{24}\:=\:\mathrm{y}\: \\…
Question Number 30529 by abdo imad last updated on 22/Feb/18 $${let}\:{f}\left({x}\right)={e}^{−{x}^{\mathrm{2}} } \:\:{prove}\:{that}\:{f}^{\left({n}\right)} \:{is}\:{at}\:{form} \\ $$$${f}^{\left({n}\right)} =\:{p}_{{n}\:} \:{e}^{−{x}^{\mathrm{2}} } \:\:{find}\:{relation}\:{between}\:{p}_{{n}} {and}\:{p}_{{n}+\mathrm{1}\:} . \\ $$$$\left.\mathrm{2}\right)\:{find}\:{p}_{\mathrm{0}} \:,{p}_{\mathrm{1}}…
Question Number 30523 by abdo imad last updated on 22/Feb/18 $$\:\left(\alpha_{{k}} \right)_{\mathrm{0}\leqslant{k}\leqslant{n}−\mathrm{1}} {are}\:{roots}\:{of}\:\:{x}^{{n}} −\mathrm{1}\:\:{simplify} \\ $$$$\prod_{{n}} =\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:\left({x}+\alpha_{{k}} {y}\right)\:. \\ $$ Terms of Service…