Is x the square of an integer? (1) x = 12k + 6, where k is a positive integer (2) x = 3q + 9, where q is a positive integer

No

Step-by-step explanation:

(1) x = 12k + 6, where k is a positive integer,

then x = 6 * (2k + 1)

Assume x is the square of 6 (6*6), then 2k+1=6 and 2k = 5 gives k=2.5

But k should be a positive integer, therefore the assumption is wrong.

(2) x = 3q + 9, where q is a positive integer,

then x = 3 * (q+3)

Assume x is the square of 3 (3*3), then q+3 = 3 gives q=0

But q should be a positive integer, not 0, therefore the assumption is wrong.