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      Question

      In the question, two equations I and II are given. You

      have to solve both the equations to establish the correct relation between x and y and choose the correct option. I. (x + 2)Β² = 15x – 26 II. (y – 6)Β² = 6 – y
      A x > y Correct Answer Incorrect Answer
      B x < y Correct Answer Incorrect Answer
      C x β‰₯ y Correct Answer Incorrect Answer
      D x ≀ y Correct Answer Incorrect Answer
      E x = y or the relationship cannot be established Correct Answer Incorrect Answer

      Solution

      ATQ,

      (x + 2) Β² = 15x – 26

      xΒ² + 4x + 4 = 15x – 26

      xΒ² – 11x + 30 = 0

      xΒ² – 5x – 6x + 30 = 0

      x(x – 5) – 6(x – 5) = 0

      (x – 5)(x – 6) = 0

      x = 5, 6

      From II:
      (y – 6) Β² = 6 – y

      yΒ² – 12y + 36 = 6 – y

      yΒ² – 11y + 30 = 0

      yΒ² – 5y – 6y + 30 = 0

      y(y – 5) – 6(y – 5) = 0

      (y – 5)(y – 6) = 0

      y = 5, 6

      So, the relationship cannot be established.

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