Question

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

Answer 1

No

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.