# Find out maximum as well as minimum

Algebra Level 5

$\large{ p\leq 4(a^3+b^3+c^3+d^3)-(a^4+b^4+c^4+d^4)\leq q }$

Let the real numbers $$a,b,c,d$$ satisfy the relations $$a+b+c+d=6$$ and $$a^2+b^2+c^2+d^2=12$$. If above inequality is satisfied for some positive integers $$p$$ and $$q$$. Find the value of $$p+q$$

×