Problem
ALG-B1-M01-P021 Three Numbers and a Product
#21
★★★★☆ Level 4 of 5
Let \(a+b+c=0\) and \(abc=2\). Find \(a^3+b^3+c^3\).
Use the identity for the sum of three cubes.
Since \(a+b+c=0\), the identity gives \(a^3+b^3+c^3=3abc\).
Given \(abc=2\), we get \(a^3+b^3+c^3=6\).
The computation is simple, but recognising the condition matters.