You don't need the _same_ answer for 1 and 2. It is sufficient if 1 and 2
each yield a unique answer.

Bottom-line you should be able to arrive at a unique value for k^2 - k
using 1 or 2 or both.

Okay, so 1) and 2) has different numbers for K, (if my calcuation was correct), K^2-k would be also different numbers - but it is still sufficient to answer D)?

No need to calculate the value of k. we can approach the question in a different way

1) k - 1/k =1

multiply with k gives k^2 - 1 =k

now rearraange

K^2-k =1 >>Ans

Now take case 2)

2k-1 = root5

Square the equation ie (2k-1)^2 =5

i.e.

4k^2-4k+1=5

4k^2-4k-4=0 (after re-arranging)

Divide by 4 >> k^2-k-1=0

Re-arranging gives k^2-k=1 >> Ans.

Both cases give the same result ... so Ans is D