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Question:

Consider the pair of equations: x² – xy – x = 22 and y² – xy + y = 34. If x > y, then x – y equal.

Explanation:

Given x² – xy – x = 22 and y² – xy + y = 34.

Adding both the equations

⇒ x² + y² – 2xy - (x – y) = 56

⇒ (x - y)² – (x - y) = 56

⇒ (x - y)(x - y - 1) = 56

Let (x – y) = a [a > 0 since x > y]

⇒ a(a - 1) = 56

⇒ a² – a – 56 = 0

⇒ (a – 8)(a + 7) = 0

⇒ a = 8 or -7 (rejected)

∴ a = x - y = 8

Hence, option (a).