Question

Prove that x2 – x is divisible by 2 for all positive integer x.

Answer 1

x^2 - 1
=>x(x-1)
Now in case 1 let the x ve even.
Then, x-1 will be odd and x will be even so, it is divisible by 2 as one factor of (x^2-x) is divisible by 2 and that factor is x.

Now in case 2 let x be odd then x-1 is even and x is odd.
so, it is divisible by 2 as one factor of (x^2-x) is divisible by 2 and that factor is x-1.

Answer 2

Answer:

Step-by-step explanation:

X(x-1)

2n(2n-1) div. By 2

Now for odd

(2n-1-1)(2n-1) div. By 2

Hence wee can say that 2 is the right solution

Please mark me birliant.

Short answer. Hope it helps.