Discussion

Explanation:

Consider statement A:

(x+y)(x+y)xy=4
∴ (x + y)2 = 4xy

∴ x2 + y2 + 2xy − 4xy = 0

∴ (x − y)2 = 0

∴ x = y

∴ Statement A alone is sufficient.

Consider statement B:

(x – 50)2 = (y – 50)2

∴ Either (x − 50) = (y − 50) or (x − 50) = −(y − 50)

∴ Either x = y or x + y = 100, which gives infinite values for x and y.

∴ Statement B alone is not sufficient.

Hence, option (a).

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