Multiple choice

$I. (x^2 = 6+x) (II. (y^2 - 2y = 8)$ Solve the given equations and find the relationship between x and y.

  1. If x > y

  2. If x ≥ y

  3. If x < y

  4. If x ≤ y

  5. If x = y or relationship cannot be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Solve equation I: x^2 - x - 6 = 0 gives x = (1 ± √25)/2 = (1 ± 5)/2, so x = 3 or x = -2. Solve equation II: y^2 - 2y - 8 = 0 gives y = (2 ± √36)/2 = (2 ± 6)/2, so y = 4 or y = -2. Comparing values: when x = 3 and y = 4, x < y; when x = 3 and y = -2, x > y; when x = -2 and y = 4, x < y; when x = -2 and y = -2, x = y. Since the relationship varies, option E is correct.

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