Question

2. Prove that x2 – x is divisible by 2 for all positiveinteger x. ​

Answer 1

Step-by-step explanation:

if x is an even integer 2n

x²-2x = 4n²-2n

= 2×(2n²-n)

hence divisible by 2

if x is odd integer 2n+1

x²-2x = (2n+1)² - (2n+1)

= 4n²+4n+1 - 2n - 1

= 4n²+2n

=2×(2n² + n)

hence divisible by 2 again

therefore for any positive integer x, x²-x is divisible by 2