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:
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 = [tex]\frac{1}{x}[/tex].
According to question :
[tex]x +\frac{1}{x}[/tex] = [tex]\frac{4}{3}[/tex].
On multiplication both sides by x
x² + 1 = [tex]\frac{4x}{3}[/tex].
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
