a^4+b^4+c^4+d^4-4abcd=0
a^4+b^4-2a^2b^2+c^4+d^4-2c^2d^2-4abcd+2a^2b^2+2c^2d^2=0
(a^2-b^2)2+(c^2-d^2)2+2(ab-cd)2=0
当a、b、c、d四个数同号时,
a=b=c=d
a^4+b^4+c^4+d^4-4abcd=0
a^4+b^4-2a^2b^2+c^4+d^4-2c^2d^2-4abcd+2a^2b^2+2c^2d^2=0
(a^2-b^2)2+(c^2-d^2)2+2(ab-cd)2=0
当a、b、c、d四个数同号时,
a=b=c=d