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      Question

      If the sum of x , y , and z is 9, and the sum of their

      squares is 18, then determine the value of the expression xy + yz + zx .
      A 42 Correct Answer Incorrect Answer
      B 31.5 Correct Answer Incorrect Answer
      C 15 Correct Answer Incorrect Answer
      D 36 Correct Answer Incorrect Answer

      Solution

      (x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx) So, 92 = 18 + 2(xy + yz + zx) Or, 81 = 18 + 2(xy + yz + zx) So, 2(xy + yz + zx) = 81 - 18 = 63 So, (xy + yz + zx) = (63/2) = 31.5

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