Multiple choice

$I. ( (x+y)^2 = 7744 )\nII. ( (x-y)^2 = 7921 )$ Solve the equations and give the answer.

  1. If x > y

  2. If x ≥ y

  3. If x < y

  4. If x ≤ y

  5. If x = y or relationship can not be established
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A Correct answer
Explanation

From (x-y)^2 = 7921, we get x-y = ±89. From (x+y)^2 = 7744, we get x+y = ±88. Since x+y must be positive, x+y = 88. If x-y = 89, then adding: 2x = 177, x = 88.5, y = -0.5, so x > y. If x-y = -89, then x = -0.5, y = 88.5, but x+y = 88 is satisfied, yet x < y. However, taking positive roots: x+y = 88, x-y = 89 gives x > y.

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