Question
If P = 7 + 4√3 and PQ = 1, then what is the value of
1/P2 + 1/Q2?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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