Question

If x is a positive integer, then show that (2x-1)(2x)(2x+1) is always divisible by 6

Answer 1

Answer:

Step-by-step explanation:

2x - 1, 2x and 2x + 1 are Three consecutive positive integers, thus EXACTLY one of them is divisible by 3 and AT LEAST one of them is divisible by 2. Since HCF(2 , 3) = 1

it follows that the Product (2x - 1) 2x (2x + 1) is divisible by 2 × 3, that is divisible by 6.