Question

一道集合类问题？

如图

Answer 1

x/|x| +y/|y|+z/|z| + |xyz|/(xyz)

case 1: x>0 and y>0 and z>0

x/|x| +y/|y|+z/|z| + |xyz|/(xyz)

=x/x +y/y+z/z + xyz/(xyz)

=1+1+1+1

=4

case 2: x<0 and y>0 and z>0

x/|x| +y/|y|+z/|z| + |xyz|/(xyz)

=x/(-x) +y/y+z/z + xyz/(-xyz)

=-1+1+1-1

=0

case 3: x>0 and y<0 and z>0

x/|x| +y/|y|+z/|z| + |xyz|/(xyz)

=x/x +y/(-y)+z/z + xyz/(-xyz)

=1-1+1-1

=0

case 4: x>0 and y>0 and z<0

x/|x| +y/|y|+z/|z| + |xyz|/(xyz)

=x/x +y/y+z/(-z) + xyz/(-xyz)

=1+1-1-1

=0

case 5: x<0 and y<0 and z>0

x/|x| +y/|y|+z/|z| + |xyz|/(xyz)

=x/(-x) +y/(-y)+z/z + xyz/(xyz)

=-1-1+1+1

=0

case 6: x<0 and y>0 and z<0

x/|x| +y/|y|+z/|z| + |xyz|/(xyz)

=x/(-x) +y/y+z/(-z) + xyz/(xyz)

=-1+1-1+1

=0

case 7: x>0 and y<0 and z<0

x/|x| +y/|y|+z/|z| + |xyz|/(xyz)

=x/x +y/(-y)+z/(-z) + xyz/(xyz)

=1-1-1+1

=0

case 8: x<0 and y<0 and z<0

x/|x| +y/|y|+z/|z| + |xyz|/(xyz)

=x/(-x) +y/(-y)+z/(-z) + xyz/(-xyz)

=-1-1-1-1

=-4

x/|x| +y/|y|+z/|z| + |xyz|/(xyz)

={ -4,0 ,4}

Answer 2

xyz里负数的个数为3时，原式=-1 + -1 + -1 + -1=-4
个数为2时，原式=-1 + -1+1+1=0
个数为1时，原式=-1+1+1+ -1=0
个数为0时，原式=1+1+1+1=4