Strange numbers

Algebra Level 5

Let $a$ , $b$ , and $c$ be non-zero real numbers such that

$(ab+bc+ca)^3 = abc (a+b+c)^3.$

Which of the following is definitely true about $a$ , $b$ and $c$ ?

Relevant wikis:

Arithmetic sequence.
Geometric sequence.
Harmonic sequence.

None of the other choices They are in a arithmetic sequence They are in a harmonic sequence They are in a geometric sequence They are in two or more of the other choices

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.