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      Question

      Solve the quadratic equations and determine the relation

      between x and y: Equation 1: 4x² - 12x + 9 = 0 Equation 2: 2y² + 10y + 12 = 0
      A x > y Correct Answer Incorrect Answer
      B x ≥ y Correct Answer Incorrect Answer
      C x < y Correct Answer Incorrect Answer
      D x ≤ y Correct Answer Incorrect Answer
      E x = y or no relation Correct Answer Incorrect Answer

      Solution

      From equation 1: 4x² - 12x + 9 = 0 Dividing by 4: x² - 3x + (9/4) = 0 Using the quadratic formula: x = [3 ± √(3² - 4(1)(9/4))]/2 x = [3 ± √(9 - 9)]/2 = 3/2 (double root). From equation 2: 2y² + 10y + 12 = 0 Dividing by 2: y² + 5y + 6 = 0 Factorizing: (y + 3)(y + 2) = 0 So, y = -3 or y = -2. Comparing x and y: x = 3/2, y = -3, x > y x = 3/2, y = -2, x > y Correct option: A) x > y

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