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      Question

      x + y = 4, xy = 2, y + z = 5, yz = 3, z + x = 6 and xz

      =4, then find the value of x 3  + y 3  + z 3  – 3xyz.
      A 1755/8 Correct Answer Incorrect Answer
      B 1735/8 Correct Answer Incorrect Answer
      C 1775/8 Correct Answer Incorrect Answer
      D None of the above Correct Answer Incorrect Answer

      Solution

      Since, x 3  + y 3  + z 3  – 3xyz = (x + y + x){(x + y + z) 2  – 3(xy + yz + zx)}

      So, x + y + z = (4 + 5 + 6)/2 = 15/2

      x 3  + y 3  + z 3  – 3xyz = (15/2) × {225/4 – 3 × 9} = 15/2 × 117/4 = 1755/8

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