Category: Algebra

Question Number 30583 by abdo imad last updated on 23/Feb/18 $${decompose}\:{F}\:=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{{n}} }\:{inside}\:{C}\left[{x}\right].{n}\:{from}\:{N}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 30582 by abdo imad last updated on 23/Feb/18 $${x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:{x}_{\mathrm{3}\:} \:{are}\:{roots}\:{of}\:{the}\:{polynomial}\:{x}^{\mathrm{3}} \:−{x}+\mathrm{1}\:{find} \\ $$$${the}\:{polynomial}\:{wich}\:{have}\:{for}\:{roots}\:{x}_{\mathrm{1}} ^{\mathrm{3}} \:,{x}_{\mathrm{2}} ^{\mathrm{3}} \:{and}\:{x}_{\mathrm{3}} ^{\mathrm{3}} \:\:. \\ $$…

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 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 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