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Suppose the number is x. Then x + 5/x = 6

Multiplying throughout by x, x2+5 = 6x or x2 - 6x + 5 = 0

which can be factorised into (x-1)*(x-5)=0

So x = 1 (and 5 times its reciprocal is 5)

or x = 5 (and 5 times its reciprocal is 1).

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