$a\ne b$ what about $a^3$ and $b^3$ .

Algebra Level 3

Is it possible if $a\ne b$ then $a^3=b^3$ ?

Yes, number

a

and

b

exist No, no such number exist

2 solutions

Achmad Damanhuri
Oct 13, 2019

It is possible for a complex number. for example let $a=\frac{3+3\sqrt{-3}}{2}$ and $b=\frac{3-3\sqrt{-3}}{2}$ so then $a^3=-27=b^3$

A Former Brilliant Member
Oct 13, 2019

Cube roots of any number are examples of this.

did you mean it like this? $\sqrt[3]{4} \ne \sqrt[3]{5}$ so is it $(\sqrt[3]{4})^3=(\sqrt[3]{5})^3$

Achmad Damanhuri - 1 year, 8 months ago

No. I meant to say that the three cube roots of, say $4$ , are not equal, even though their cubes are equal.

A Former Brilliant Member - 1 year, 8 months ago