Multiple choice

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer. I. (x + 22) (x – 22) = – 123 II. y2 – 43y + 462 = 0

  1. if x > y

  2. if x ≤ y

  3. if x ≥ y

  4. if x < y

  5. if x = y or relationship between x and y can't be established
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

I: x^2 - 484 = -123 => x^2 = 361 => x = 19 or -19. II: y^2 - 43y + 462 = 0 => (y-21)(y-22) = 0 => y = 21 or 22. Comparing values, x < y in all cases.

AI explanation

Using the difference of squares formula, the first equation becomes x2 - 484 = -123, which simplifies to x2 = 361 and yields x = 19 or -19. Factoring the second equation y2 - 43y + 462 = 0 gives (y - 21)(y - 22) = 0, so the roots are y = 21 and y = 22. Since 19 is less than both 21 and 22, and -19 is also less than both, x is always less than y. Therefore, x < y.

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