Multiple choice

Directions: In this question, two equations numbered I and II are given. You have to solve both the equations and mark the correct answer. (I) x + 2 = x2 (II) 35y + 2 = 37y2

  1. x > y

  2. x < y

  3. x ≥ y

  4. x = y or no relationship can be established between 'x' and 'y'

  5. x ≤ y
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Equation I: x^2 - x - 2 = 0 => (x-2)(x+1) = 0, so x = 2 or -1. Equation II: 37y^2 - 35y - 2 = 0 => (37y + 2)(y - 1) = 0, so y = 1 or -2/37. Comparing the sets {2, -1} and {1, -0.054}, no consistent relationship exists (e.g., 2 > 1 but -1 < 1).

AI explanation

Rearranging the first equation gives x2 - x - 2 = 0, which factors into (x - 2)(x + 1) = 0 to yield roots x = 2 or x = -1. Rearranging the second equation gives 37y2 - 35y - 2 = 0, which factors into (y - 1)(37y + 2) = 0 to yield roots y = 1 or y = -2/37. Comparing the values, x = 2 is greater than both y values, but x = -1 is less than both y values. Therefore, no relationship can be established.

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