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      Question

      If p = 27 - q - r and pq + r(q + p) = 168, then find

      the value of (p² + q² + r²).
      A 381 Correct Answer Incorrect Answer
      B 387 Correct Answer Incorrect Answer
      C 393 Correct Answer Incorrect Answer
      D 399 Correct Answer Incorrect Answer

      Solution

      We have, p = 27 - q - r So, p + q + r = 27 And, pq + r(q + p) = 168 Or, pq + qr + pr = 168 Using, (p + q + r)² = p² + q² + r² + 2(pq + qr + pr) So, 27² = (p² + q² + r²) + 2 × 168 Or, 729 = (p² + q² + r²) + 336 Or, p² + q² + r² = 729 - 336 Or, p² + q² + r² = 393

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