Question

The sum of a positive integer, x, and its inverse is 4/3 find the integer.

Answer 1

Let x represent the integer.

Then x + 1/x = 4/3. Find x.

Multiply all 3 terms by 3x to clear the fractions:

3x^2 + 3 = 12x/3

3x^2 - 4x + 3 = 0

Apply the quadratic formula: a=3, b= -4, c = 3.

Then

4 plus or minus sqrt(16-4(3)(3))

x = -----------------------------------------------

6

4 plus or minus sqrt(-20)

= --------------------------------------

6

Unfortunately, these roots are not integer; worst yet, they are complex.

Answer 2

x = 1/3

Explanation:

Given : The sum of a positive integer, x, and its inverse is 4/3 .

To find : find the integer.

Solution : We have given The sum of a positive integer, x, and its inverse is 4/3 .

Positive number = x

Inverse of positive number x is =
`(1)/(x)`.

According to question :

`x +(1)/(x)` =
`(4)/(3)`.

On multiplication both sides by x

x² + 1 =
`(4x)/(3)`.

On multiplying both sides by 3

3x² + 1 = 4x .

3x²- 4x + 1 = 0.

On factoring

3x²-3x -x + 1 = 0.

3x (x -1) -1 (x-1) = 0

On grouping

(3x -1)( x-1) = 0

3x - 1 = 0

x = 1/3

x -1 = 0 .

x = 1.

Therefore, x = 1/3