4个实数a、b、c、d,满足下列条件:a + b + c + d = 1a + b×c×d = 1000b + a×c×d = 1000c + a×b×d = 1000d + a×b×c = 1000求a×b×c×d?

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4个实数a、b、c、d,满足下列条件:a + b + c + d = 1a + b×c×d = 1000b + a×c×d = 1000c + a×b×d = 1000d + a×b×c = 1000求a×b×c×d?

4个实数a、b、c、d,满足下列条件:a + b + c + d = 1a + b×c×d = 1000b + a×c×d = 1000c + a×b×d = 1000d + a×b×c = 1000求a×b×c×d?
4个实数a、b、c、d,满足下列条件:
a + b + c + d = 1
a + b×c×d = 1000
b + a×c×d = 1000
c + a×b×d = 1000
d + a×b×c = 1000
求a×b×c×d?

4个实数a、b、c、d,满足下列条件:a + b + c + d = 1a + b×c×d = 1000b + a×c×d = 1000c + a×b×d = 1000d + a×b×c = 1000求a×b×c×d?
设abcd=k
则a,bcd是x^2-1000x+k=0的两根
同理b,acd,c,abd,d,abc也是
所以a=b,bcd=acd或a=acd,b=bcd
得到a=b或cd=1
同理a,b,c,d之间的关系都能得到
若a=b=c=d,
a=b=c=d=1/4不符合条件
若a=b=c,ab=ac=bc=1
a=1,b=1,c=1,d=-2不符合条件
若a=b,ad=ac=bd=bc=1
a+1/a=1/2,不符合条件
若ab=ac=ad=bc=bd=cd=1
得到a=b=c=d,不符合条件
所以貌似不存在这样的数