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

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.

x = 1/3

Step-by-step 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 = .

According to question :

= .

On multiplication both sides by x

x² + 1 =  .

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

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,

faster, im not sure why but i know it is faster