Multiple choice

Derive the relationship between x and y by solving the given equations: x2 - 19x + 84 = 0 y2 - 25y + 156 = 0

  1. x > y

  2. x < y

  3. x ≥ y

  4. x ≤ y

  5. x = y or relationship can not be established.
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D Correct answer
Explanation

x^2 - 19x + 84 = 0 factors to (x-7)(x-12) = 0, so x = 7, 12. y^2 - 25y + 156 = 0 factors to (y-12)(y-13) = 0, so y = 12, 13. Comparing values: 7 < 12, 7 < 13, 12 = 12, 12 < 13. Thus, x <= y.

AI explanation

Factoring the first equation x2 - 19x + 84 = 0 provides the roots x = 12 and x = 7. Factoring the second equation y2 - 25y + 156 = 0 provides the roots y = 13 and y = 12. Since the maximum value of x is 12 and the maximum value of y is 13, x is always less than or equal to y, establishing the relationship x y.

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