Question 59
Real numbers $a,b,c,d$ satisfy $a+b+c+d=6$ and $a^2+b^2+c^2+d^2=12$. Prove
$$36\le4(a^3+b^3+c^3+d^3)-(a^4+b^4+c^4+d^4)\le48.$$
$$36\le4(a^3+b^3+c^3+d^3)-(a^4+b^4+c^4+d^4)\le48.$$
MathNet 2011 Question 59
Math Olympiad Vault · MathNet 2011