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      Question

      If p = 25 - q - r and pq + r(q + p) = 189, then find the

      value of (p² + q² + r²).
      A 243 Correct Answer Incorrect Answer
      B 247 Correct Answer Incorrect Answer
      C 251 Correct Answer Incorrect Answer
      D 257 Correct Answer Incorrect Answer

      Solution

      We have, p = 25 - q - r So, p + q + r = 25 And, pq + r(q + p) = 189 Or, pq + qr + pr = 189 Using, (p + q + r)² = p² + q² + r² + 2(pq + qr + pr) So, 25² = (p² + q² + r²) + 2 × 189 Or, 625 = (p² + q² + r²) + 378 Or, p² + q² + r² = 625 - 378 Or, p² + q² + r² = 247

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