x 3 x^3 =1

Algebra Level 2

Is x=1 the only solution for x 3 x^3 =1?

Yes No

Jesse Li by Jesse Li , 16, USA

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1 solution

Steven Chase
Oct 14, 2018

Solutions are:

1 + 0 j − 1 2 + 3 2 j − 1 2 − 3 2 j 1 + 0 j \\ -\frac{1}{2} + \frac{\sqrt{3}}{2} j \\ -\frac{1}{2} - \frac{\sqrt{3}}{2} j

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I believe you mean i i instead of j j . There are complex roots, not quaternion roots.

Blan Morrison - 2 years, 8 months ago

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That's my habit as an engineer. We use j

Steven Chase - 2 years, 8 months ago

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Ah! Just googled it and realized i i stands for current. Very interesting...

Also, as it turns out, j 2 = − 1 ~j^2=-1 anyway.

Blan Morrison - 2 years, 8 months ago

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