If $x_1 x_2 x_3 = 4(4 + x_1 + x_2 + x_3)$, then what is the value of $[1/(2 + x_1)] + [1/(2 + x_2)] + [1/(2 + x_3)]$?

x1.x2.x3 = 4(4 + x1 + x2 + x3)

Put x2 = 1 and x3 = 1;

⇒ x1 = 4(4 + x1 + 1 + 1)

⇒ x1 = 16 + 4x1 + 8

⇒ x1 = -8

Putting all these values;

[1/(2 + x1)] + [1/(2 + x2)] + [1/(2 + x3)]

⇒ -1/6 + 1/3 + 1/3

⇒ 1/2