Multiple choice

I. $x^2-x-42=0$ II. $y^2-17y+72=0$ to solve both the equations to find the values of $x$ and $y$?

  1. $x < y$
  2. $x > y$
  3. $x \geq y$
  4. If $x = y$ or the relationship between $x$ and $y$ cannot be established.
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A Correct answer
Explanation

x^2 - x - 42 = 0 -> (x-7)(x+6) = 0 -> x = 7, -6. y^2 - 17y + 72 = 0 -> (y-8)(y-9) = 0 -> y = 8, 9. Comparing values: 7 < 8, 7 < 9, -6 < 8, -6 < 9. Thus x < y.

AI explanation

Factoring the first equation x^2 - x - 42 = 0 gives x = 7 or x = -6. Factoring the second equation y^2 - 17y + 72 = 0 gives y = 8 or y = 9. Comparing the values, both 7 and -6 are less than 8 and 9, so x is always less than y.

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