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      Question

      If x = 28 - y - z and xy + z(x + y) = 238, then find

      the value of (x 2 + y 2 + z 2).
      A 292 Correct Answer Incorrect Answer
      B 308 Correct Answer Incorrect Answer
      C 296 Correct Answer Incorrect Answer
      D 304 Correct Answer Incorrect Answer

      Solution

      We have, x = 28 - y - z

      So, x + y + z = 28

      And, xy + z(x + y) = 238

      Or, xy + yz + xz = 238

      Using, (x + y + z)2 = x2  + y2 + z2 + 2(xy + yz + xz)

      So, 282 = (x2 + y2 + z2) + 2 X 238

      Or, x2 + y2 + z2 = 784 - 476

      Or, x2 + y2 + z2 = 308

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