Multiple choice

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and give answer. I. x2 - 16x + 60 = -3 II. y2 - 12y + 25 = -10

  1. if x > y

  2. if x ≥ y

  3. if x < y

  4. if x ≤ y

  5. if x = y or Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

I: x^2 - 16x + 63 = 0. (x-7)(x-9) = 0, so x = 7, 9. II: y^2 - 12y + 35 = 0. (y-5)(y-7) = 0, so y = 5, 7. Comparing: x=7, y=5 (x>y); x=7, y=7 (x=y); x=9, y=5 (x>y); x=9, y=7 (x>y). Thus x >= y.

AI explanation

Rearranging both equations gives x2 - 16x + 63 = 0 and y2 - 12y + 35 = 0. Using the factorization method, the first equation becomes (x - 7)(x - 9) = 0, yielding x = 7 or x = 9. The second equation becomes (y - 5)(y - 7) = 0, yielding y = 5 or y = 7. Because the maximum value of x is greater than y and the minimum value of x is equal to y, the overall relationship is x is greater than or equal to y.

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