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      Question

      If p = 35 - q - r and pq + r(q + p) = 315, then find

      the value of (p² + q² + r²).
      A 575 Correct Answer Incorrect Answer
      B 585 Correct Answer Incorrect Answer
      C 595 Correct Answer Incorrect Answer
      D 605 Correct Answer Incorrect Answer

      Solution

      We have, p = 35 - q - r So, p + q + r = 35 And, pq + r(q + p) = 315 Or, pq + qr + pr = 315 Using, (p + q + r)² = p² + q² + r² + 2(pq + qr + pr) So, 35² = (p² + q² + r²) + 2 × 315 Or, 1225 = (p² + q² + r²) + 630 Or, p² + q² + r² = 1225 - 630 Or, p² + q² + r² = 595

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