Cube Roots of 1

Algebra Level 4

Find Value of this simple Equation


The answer is 3.

Ahmed Ȝbd EL MøȜez by Ahmed Ȝbd EL MøȜez , 24, Egypt

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2 solutions

This was somewhat more of a trial and error question; for x = 3 x = 3 we have:

3 = ω 6 + ω 3 + 1 = 1 + 1 + 1 = 3 3 = \omega^{6} + \omega^{3} + 1 = 1 + 1 + 1 = 3 .

To prove it is the only root is slightly complicated, but I'm not jumping into this matter.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Using the AM>GM we have the following process

0 Helpful 0 Interesting 0 Brilliant 0 Confused

@Jesus Ulises Avelar how do you write :- 3w^x=(x/3)^2+x/3+1

AMAN KUMAR - 6 years, 2 months ago

If you can't use AM-GM for negative reals , how can you use it for complex nos. ?

Nihar Mahajan - 5 years, 7 months ago

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