Multiple choice

In the following question two equations numbered I and II are given. You have to solve both the equations and give answer.(I. x^2 + 2x - 8 = 0 ) (II. y^2 - 2 = 7)

  1. $\(x > y\)$
  2. $\(x \ge y\)$
  3. $\(x < y\)$
  4. $\(x \le y\)$

  5. x = y, or relation cannot be established
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E Correct answer
Explanation

Solving equation I gives x² + 2x - 8 = 0, which factors to (x+4)(x-2) = 0, so x = -4 or x = 2. Solving equation II gives y² - 2 = 7, so y² = 9 and y = -3 or y = 3. When comparing x = -4 with y = -3, we get x < y. When comparing x = 2 with y = 3, we get x < y. However, we could also have x = 2 compared to y = -3, giving x > y. Since the relationship is not consistent across all combinations, no definite relation can be established.

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