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      Question

      If p = 32 - q - r and pq + r(q + p) = 255, then find

      the value of (p² + q² + r²).
      A 494 Correct Answer Incorrect Answer
      B 502 Correct Answer Incorrect Answer
      C 508 Correct Answer Incorrect Answer
      D 514 Correct Answer Incorrect Answer

      Solution

      We have, p = 32 - q - r So, p + q + r = 32 And, pq + r(q + p) = 255 Or, pq + qr + pr = 255 Using, (p + q + r)² = p² + q² + r² + 2(pq + qr + pr) So, 32² = (p² + q² + r²) + 2 × 255 Or, 1024 = (p² + q² + r²) + 510 Or, p² + q² + r² = 1024 - 510 Or, p² + q² + r² = 514

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