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    Question

    If p = 40 - q - r and pq + r(p + q) = 400, then find the

    value of (p² + q² + r²).
    A 810 Correct Answer Incorrect Answer
    B 750 Correct Answer Incorrect Answer
    C 800 Correct Answer Incorrect Answer
    D 768 Correct Answer Incorrect Answer

    Solution

    We have, p = 40 - q - r
    So, p + q + r = 40
    And, pq + r(p + q) = 400
    Or, pq + qr + pr = 400
    Using, (p + q + r)² = p² + q² + r² + 2(pq + qr + pr)
    40² = (p² + q² + r²) + 2 × 400
    1600 = (p² + q² + r²) + 800
    p² + q² + r² = 800

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