若a、b、c、d是四边形ABCD的四边,且满足a^4+b^4+c^4+d^4-4abcd=0,问此为何种四边形

菱形 a^4+b^4+c^4+d^4-4abcd=0a^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所以a^2-b^2=0c^2-d^2=0 ab-cd=0得出a=b=c=d