Question

given a^4 +a^3+a^2+a+1=0 then find the value of a^2000+a^2010 +1

Answer 1

Value of $a^{2000}+a^{2010} +1$    is 3

Step-by-step explanation:

given data

$a^4 +a^3+a^2+a+1=0$  

to find out

$a^{2000}+a^{2010} +1$  

solution

first know equation is

$a^4+a^3+a^2+a+1 = 0$              ...............................a

now we multiply this equation with a we will get

$a^5+a^4+a^3+a^2+a = 0$              ...............................b

now when we Subtract equation b by a we will get

$a^5-1 = 0$

so here a will be

$a^5 = 1$     ..........................c

and now we take here equation

$a^{2000}+a^{2010} +1$    

that is express as

$a^{5(400)}+a^{5(402)}+1$

put here equation c value we get

(1)^{400}+(1)^{402}+1  

solve it we get

= 1+1+1

= 3

so value of $a^{2000}+a^{2010} +1$    is 3

Learn more :

find the value of a^2000+a^2010 +1

1. https://brainly.in/question/11664005