Problem
ALG-B1-M12-P026 Variant 7, Problem 2
#26
★★★★★ Level 5 of 5
Find \(a,b,c\) if \(a+b+c=0\), \(a^2+b^2+c^2=18\), \(a^3+b^3+c^3=0\).
\(3abc=0\).
\(abc=0\), one variable is \(0\), the other two are opposite and their squares give \(18\). Answer: permutations of \((3,-3,0)\).
Mock olympiad problem. Tags: sum-zero.