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28 February, 03:49

A positive real number is 1 more than its reciprocal. Find the number.

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  1. 28 February, 04:28
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    Let the number be x, then

    x = 1 + 1/x

    x^2 = x + 1

    x^2 - x = 1

    x^2 - x + 1/4 = 1 + 1/4

    (x - 1/2) ^2 = 5/4

    x - 1/2 = + or - 5/4

    x = 5/4 + 1/2 or - 5/4 + 1/2

    x = 7/4 or x = - 3/4

    But x is positive,

    Therefore, x = 7/4 = 1.75
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