(18)

Given,

A = {1, 2, 3..., 10} B = {0,1, 2,4}

(a, b) A x A such that

2(a-b) 2 + 3(a-b)-k = 0

where fee {0,1,2,3,4}

Now finding discriminant D = 9 - 4 x 2(-k)

And 9 - 4x2(-k) a perfect square for any possible (a, b) as (a - b) will be a integer,

So, 9 + 8k is a perfect square

k = 0 or k = 2

Now for k = 0,

2(a-b) 2 + 3(a-b) =0

(a - b) [2(a - b) 2 + 3] = 0

a - b = 0 (a, b) {(1,1), (2, 2) .... (10,10)}

Total 10 elements belonging to R.

And, a – b = is not possible

Now for k = 2,

2(a - b) 2 + 3(a - b)-2 = 0

a - 6 = -2 or a - b = (not possible)

Now for a - b = -2 possible pair will be,

(a, b) {(1,3), (2,4) .... (8,10)}

8 elements belonging to R

Total number of elements will be = 18

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