a^4+ b^4+ c^4+ d^4=4abcd ==> (a^2-b^2)^2+(c^2-d^2)^2+2(ab-cd)^2= =(a^2-c^2)^2+(b^2-d^2)^2+2(ac-bd)^2=0,a,b,c,d为实数,则a^2-b^2=0,c^2-d^2=0,ab-cd=0,a^2-c^2=b^2-d^2=ac-bd=0==》 a^2=b^2=c^2=d^2,ab=cd,ac=bd.1）a=b=c=d=0.2）a,b,c,d≠0,而其中3个同号,ab,cd异号,和ab=cd矛盾.所以只能两两同号,或4个同号,而|a|=|b|=|c|=|d|,比如：a=b=1,c=d=-1.3）若4个同号则a=b=c=d.