Just 1 equation?

Algebra Level 3

If x 6 = 1 x^ 6 = 1 but x n ≠ 1 x^n \neq 1 for all positive integers n ≤ 5 n \leq 5 , which of the following must be true?

None of the rest x 3 + x 2 = − 1 x^3 + x^2 = -1 x 4 + x 2 = − 1 x^4 + x^2 = -1 x 4 + x 3 = − 1 x^4 + x^3 = -1

Calvin Lin by Calvin Lin

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2 solutions

Edwin Gray
Sep 12, 2018

If x^6 = 1, (x^2 -1)(x^4 + x^2 + 1) = 0. Since x^2 .ne.1, the other factor must = 0. Then X^4 + X^2 = -1. Ed Gray

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Archit Agrawal
Oct 22, 2016

x^4+x^2 =x^2(x^2+1) =x^2(x^4-1)/(x^2-1) =(x^6-x^2)/(x^2-1) =(1-x^2)/(x^2-1) =-1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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