Problem
ALG-B2-M06-P013 Checking the fourth-degree inequality
#13
★★★★☆ Level 4 of 5
Check the inequality \[a^4+b^4+c^4\ge abc(a+b+c)\] in the case \(b=c=1\), \(a=t\ge0\).
Hint. The difference should have the factor \((t-1)^2\).
After substitution, we get \(t^4+2\ge t(t+2)\). The difference is \(t^4-t^2-2t+2=(t-1)^2(t^2+2t+2)\ge0\).
Preparation for the full UVW proof.