Suppose the decimal 0.28 is = to 1/n +1/n^2, where n is negative. Find n.
.28 = 28 /100 = 7/25
7/25 = 1/n + 1/n^2 multiply through by n^2
(7/25)n^2 = n + 1 mutiply through by 25
7n^2 = 25n + 25
7n^2 - 25n - 25 = 0
Q Formula
n = 25 - sqrt ( 25^2 + 4 * 7 * 25) 25 - sqrt (25 [ 25 + 28 ] )
___________________________ = ______________________ =
2 * 7 14
25 - 5 sqrt (53)
_______________
14