Multiple choice

Directions: In the given question, two equations are given. You have to solve both the equations and mark the correct option. (i) X2 - 39X + 380 = 0 (ii) Y2 - 41Y + 420 = 0

  1. X < Y

  2. X > Y

  3. X ≥ Y

  4. X ≤ Y

  5. The relationship between X and Y cannot be established.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Solving X^2 - 39X + 380 = 0: (X-19)(X-20) = 0, so X = 19, 20. Solving Y^2 - 41Y + 420 = 0: (Y-20)(Y-21) = 0, so Y = 20, 21. Comparing values, 19 < 20, 19 < 21, 20 = 20, 20 < 21. Thus X <= Y.

AI explanation

For the first equation X2 - 39X + 380 = 0, we find two numbers that multiply to 380 and add to 39, which are 19 and 20, so X = 19 or X = 20. For the second equation Y2 - 41Y + 420 = 0, the numbers 20 and 21 multiply to 420 and add to 41, giving Y = 20 or Y = 21. When comparing the values, the smallest value of X (19) is less than the largest value of Y (21), but the largest value of X (20) is equal to the smallest value of Y (20). Since X is either less than or equal to the corresponding values of Y, the relationship is X ≤ Y.

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