Multiple choice

In the following questions two equations numbered I and II are given. You have to solve both the equations and ————— I. (x^{2} - 218 = 106) II. (y^{2} - 37y + 342 = 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 established
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Equation I: x² - 218 = 106, so x² = 324, which means x = ±18. Equation II: y² - 37y + 342 = 0. Using quadratic formula: y = [37 ± √(1369 - 1368)] ÷ 2 = [37 ± √1] ÷ 2 = [37 ± 1] ÷ 2. So y = 38/2 = 19, or y = 36/2 = 18. Comparing: x can be 18 or -18. y can be 19 or 18. If x = -18, then x < y (since -18 < 18 and -18 < 19). If x = 18, then x ≤ y (since 18 = 18 when y = 18, and 18 < 19 when y = 19). In all cases, x ≤ y is true. Option D is correct.

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