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    Question

    If p = 20 - q - r and pq + r(p + q) = 154, then find the

    value of (p² + q² + r²).
    A 100 Correct Answer Incorrect Answer
    B 96 Correct Answer Incorrect Answer
    C 92 Correct Answer Incorrect Answer
    D 88 Correct Answer Incorrect Answer

    Solution

    We have, p = 20 - q - r
    So, p + q + r = 20
    And, pq + r(p + q) = 154
    Or, pq + qr + pr = 154
    Using, (p + q + r)² = p² + q² + r² + 2(pq + qr + pr)
    20² = (p² + q² + r²) + 2 × 154
    400 = (p² + q² + r²) + 308
    p² + q² + r² = 92

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