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

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%