Question

The sum of a number and its reciprocal is 13/6. find the number

Answer 1

`x + (1)/(x) = (13)/(6) \text{, x} \\eq 0`

`x^(2) - (13)/(6)x + 1 = 0`

`6x^(2) - 13x + 6 = 0`

`6x^(2) -9x - 4x + 6 = 0`

`3x(2x - 3) - 2(2x - 3) = 0`

`(3x - 2)(2x - 3) = 0`

So, the numbers are: 3/2 and 2/3