Question

Get 15 points solve the question Given a4 + a3 + a2 + a + 1 = 0. Find the value a2000 + a2010 + 1.

Answer 1

Find the value a2000 + a2010 + 1

Answer: 3

Step-by-step explanation:

Given, $a^4+a^3+a^2+a+1=0$...............................(1)

Multiply by $a$ in equation (1),

$a^5+a^4+a^3+a^2+a=0$...............................(2)

Subtract equation (2) and (1),

$a^5-1=0$

$a^5=1$

Now, $a^{2000}+a^{2010}+1=a^{5(400)}+a^{5(402)}+1$

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

                                    $=(1)^{400}+(1)^{402}+1$

                                    $=1+1+1$

                                    $=3$

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Answer 2

Answer:

Answer is 3

Step-by-step explanation:

A⁴ + A³ + A² + A + 1 = 0

A⁴+ A³+ A²+ A = -1

Multiple both sides by a

A⁵+A⁴+A³+A²+A = 0

A⁵  - 1 = 0

A⁵ = 1

Now enjoy

put the value of 1 in a_2000+a_2010+1

1+1+1=3 is the answer