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15 September, 03:32

The difference of a positive integer and its inverse is 15/4. Find the integer.

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  1. 15 September, 04:49
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    X - 1/X = 15/4

    X/1 - 1/x = 15/4

    X • (X/1) - 1/X = 15/4

    X ^2 - 1/X = 15/4

    X • (X ^2 - 1/X) = 15/4 • X

    X^2 - 1 = 15x/4

    4 • (X ^2 - 1) = 15x/4 • 4

    4 (X^2 - 1) = 15x

    4x ^2 - 4 = 15x

    4x^2 - 15x - 4 = 0

    4x^2 - 15x = 4

    X (4x - 15) = 4.

    X = 4

    4x - 15 = 4

    4x = 19

    4x/4 = 19/4

    X = 19/4.

    I believe the solution is 4.

    4/1 - 1/4 = 15/4

    16/4 - 1/4 = 15/4

    15/4 = 15/4.
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