Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 208814 by Ismoiljon_008 last updated on 23/Jun/24

Commented by Ismoiljon_008 last updated on 23/Jun/24

$$Helpmeplease$$

Commented by Ismoiljon_008 last updated on 23/Jun/24

$$If{x}^4+x^3+x^2+x+1=0,then{x}^{71}-x^{61}+x^{51}+x^{41}+1=?$$

Answered by Rasheed.Sindhi last updated on 23/Jun/24

$$If{x}^4+x^3+x^2+x+1=0,then{x}^{71}-x^{61}+x^{51}+x^{41}+1=?$$$$x^4+x^3+x^2+x+1=0$$$$\Rightarrow (x-1)(x^4+x^3+x^2+x+1)=0$$$$x^5-1=0\Rightarrow x^5=1$$$$x^{71}-x^{61}+x^{51}+x^{41}+1$$$$={\left(x^5\right)}^{14}\cdot x-{\left(x^5\right)}^{12}\cdot x+{\left(x^5\right)}^{10}\cdot x+{\left(x^5\right)}^8\cdot x+1$$$$={\left(1\right)}^{14}\cdot x-{\left(1\right)}^{12}\cdot x+{\left(1\right)}^{10}\cdot x+{\left(1\right)}^8\cdot x+1$$$$=x-x+x+x+1=2x+1$$

Commented by Ismoiljon_008 last updated on 23/Jun/24

$$Thankyouverymuch$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com