Multiple choice

In each of the following questions two equations are given. Solve these equations and give answer : (I) (x^2 - 25 + 16 = 0) (II) (5y^2 - 40y + 60 = 0)

  1. If x < y

  2. If x > y

  3. If x ≥ y

  4. If x ≤ y

  5. If x = y or no relationship can be established between x and y.
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E Correct answer
Explanation

Solving equation (I): x² - 9 = 0 gives x = ±3. Solving equation (II): 5y² - 40y + 60 = 0, dividing by 5 gives y² - 8y + 12 = 0, so y = (8 ± √(64-48))/2 = (8 ± 4)/2, giving y = 6 or y = 2. Comparing: when x = 3, it can be less than, equal to, or greater than y depending on which y value is chosen. When x = -3, it's always less than y (which are positive). No single relationship (x < y, x > y, x ≤ y, or x ≥ y) holds for all combinations.

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