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    Question

    If P = 7 + 4√3 and PQ = 1, then what is the value of

    1/P2 + 1/Q2?
    A 196 Correct Answer Incorrect Answer
    B 194 Correct Answer Incorrect Answer
    C 206 Correct Answer Incorrect Answer
    D 182 Correct Answer Incorrect Answer

    Solution

    P = 7 + 4√3 PQ=1 Q=1/(7 + 4√3) Rationalizing the denominator i.e multiplying both numerator and denominator with 7 − 4√3 Q = 7 − 4√3 1 / P2 + 1 / Q2 = P2 + Q2 / P2Q2 = (P+Q)2 −2PQ / P2Q2 P +Q = 7 + 4√3 + 7 − 4√3 P+Q = 14 PQ = 1 Therefore = (196-2)/1 =194

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