Question
If 'x' is a positive integer such that x + 1/x = 2,
then find the value of (x3 + x2 − 2x – 6)/(4x4 + 2x2).Solution
x + 1/x  = 2 Or, x2 + 1 = 2x Or, x2 - 2x + 1 = 0 Or, (x - 1)2 = 0 So, 'x' = 1 (x3 + x2 − 2x – 6)/(4x4 + 2x2) = (13 + 12 – 2 X 1 – 6)/(4 X 14 + 2 x 12) = - 6/6 = - 1
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