Multiple choice

In each of the following questions, two equations are given. You have to solve them and determine the relationship between x and y. $( (I) \quad x^2 - 9x + 18 = 0 )$ $( (II) \quad y^2 - 11y + 30 = 0 )$

  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

Solving equation I: x² - 9x + 18 = 0 factors to (x-3)(x-6) = 0, so x = 3 or x = 6. Solving equation II: y² - 11y + 30 = 0 factors to (y-5)(y-6) = 0, so y = 5 or y = 6. When x = 6 and y = 6, we have x = y. When x = 3 and y = 5, we have x < y. When x = 3 and y = 6, we have x < y. When x = 6 and y = 5, we have x > y. Since different value combinations give different relationships, the relationship between x and y cannot be uniquely established.