Question

What number increased by its reciprocal equals 65/8 ?

Answer 1

Do this by Middle Term Break Method.

Answer 2

To find:

The number increased by its reciprocal is equal to 65/8.

Solution:

• Let the number be x and its reciprocal is 1/x.

• Therefore,

        x + 1/x = 65/8

        (x² + 1 ) / x = 65/8

        8x² + 8 = 65 x

        8x² - 65x + 8 = 0

        8x²  - 64x - x + 8 = 0

        8x(x-8) - 1(x-8) = 0

        (x-8) (8x -1) = 0

• Thus, x = 8 or x = 1/8

• Therefore the answer is 8 and 1/8.