If the coordinates of the point which is equidistant from the points obey the relation

MATHEMATICS · Subjective · CBSE · Mathematics · Introduction to Three-Dimensional Geometry · Introduction to Three-Dimensional Geometry

Problem

If the coordinates

(x, y, z)

of the point

S

which is equidistant from the points

O(0, 0, 0), A(n^5, 0, 0), B(0, n^4, 0), C(0, 0, n)

obey the relation

2(x + y + z) + 1 = 0

. If

n \in \mathbb{Z}

, then

|n| =

_____ (|.| is the modulus function).