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      Question

      If p = 28 - q - r and pq + r(q + p) = 182, then find

      the value of (p² + q² + r²).
      A 404 Correct Answer Incorrect Answer
      B 412 Correct Answer Incorrect Answer
      C 420 Correct Answer Incorrect Answer
      D 428 Correct Answer Incorrect Answer

      Solution

      We have, p = 28 - q - r So, p + q + r = 28 And, pq + r(q + p) = 182 Or, pq + qr + pr = 182 Using, (p + q + r)² = p² + q² + r² + 2(pq + qr + pr) So, 28² = (p² + q² + r²) + 2 × 182 Or, 784 = (p² + q² + r²) + 364 Or, p² + q² + r² = 784 - 364 Or, p² + q² + r² = 420

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