Multiple choice

In the following questions two equations I and II are given. You have to solve both the equations and give answer. $(I) (x^2 - 8.7x + 18.5 = 0) (II) (y^2 - 9 = 0)$

  1. If x > y

  2. If x ≥ y

  3. If x < y

  4. If x ≤ y

  5. If x = y or the relationship cannot be determined.
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A Correct answer
Explanation

Equation I: x² - 8.7x + 18.5 = 0. Using quadratic formula: x = [8.7 ± √(75.69 - 74)]/2 = [8.7 ± √1.69]/2 = [8.7 ± 1.3]/2. Solutions: x₁ = (8.7 + 1.3)/2 = 5, x₂ = (8.7 - 1.3)/2 = 3.7. Equation II: y² - 9 = 0, so y² = 9, giving y = ±3. Comparing: Both x values (3.7 and 5) are greater than both y values (3 and -3). Therefore x > y consistently.

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