A number theory problem by Srinivas Modem

Number Theory Level 3

If x,y,zx,y,z are positive integers, such that xyz+xy+xz+yz+x+y+z=384xyz + xy + xz + yz + x + y + z = 384 , find the value of x+y+zx+y+z.

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Srinivas Modem by Srinivas Modem
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