Multiple choice

In the following questions two equations numbered I and II are given. You have to solve both the equations and- x² - 34x + 288 = 0 y² - 28y + 192 = 0

  1. X ≥ Y

  2. X > Y

  3. X < Y

  4. X

  5. None of these
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A Correct answer
Explanation

The first equation has roots 18 and 16, while the second has roots 16 and 12. Comparing the corresponding larger roots gives X = 18 and Y = 16, so X ≥ Y.

AI explanation

Factor the first equation x^2 - 34x + 288 = 0 by splitting the middle term to get x^2 - 16x - 18x + 288 = 0, which gives (x - 16)(x - 18) = 0 and roots x = 16 or 18. Factor the second equation y^2 - 28y + 192 = 0 to get y^2 - 16y - 12y + 192 = 0, which gives (y - 16)(y - 12) = 0 and roots y = 16 or 12. Since both values of x are either greater than or equal to the values of y, X >= Y.

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