Problem

Source: Moldova TST 2022

Tags: inequalities



Real numbers $a, b, c, d$ satisfy $$a^2+b^2+c^2+d^2=4.$$Find the greatest possible value of $$E(a,b,c,d)=a^4+b^4+c^4+d^4+4(a+b+c+d)^2 .$$