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    Question

    If p = 30 - q - r and pq + r(q + p) = 296 then find the

    value of (p 2  + q 2  + r 2 ) .
    A 298 Correct Answer Incorrect Answer
    B 316 Correct Answer Incorrect Answer
    C 308 Correct Answer Incorrect Answer
    D 288 Correct Answer Incorrect Answer

    Solution

    We have, p = 30 - q - r
    So, p + q + r = 30
    And, pq + r(q + p) = 296
    Or, pq + qr + pr = 296
    Using, (p + q + r)  2  = p 2  + q 2  + r 2  + 2(pq + qr + pr)
    So, 30 2  = (p 2  + q 2  + r 2 ) + 2 X 296
    Or, p 2  + q 2  + r 2  = 900 - 592
    Or, p 2  + q 2  + r 2  = 308

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