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If x + (1/x )= 5 Then x2+ (1/x2 ) =52 – 2 = 23 and x3+(1/x3 ) =53 - 3 × 5 = 125 – 15 = 110 so x5+ (1/x5 ) = (x2+ 1/x2 ) (x3+1/x3 ) - (x + 1/x ) x5+ (1/x5 ) = (23 × 110) - (5) = 2530 - 5 = 2525
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