Question

The sum of a number and its reciprocal is 2 1/6 what is the number

Answer 1

Answer:

Here's your answer,I hope it helped you

Answer 2

Given:

The sum of a number and its reciprocal is$2\frac{1}{6}$.

To Find:

The value of the number.

Solution:

The given number can be solved by using the concepts of quadratic equations.

1. Let the value of the number be x.

2. It is given that the sum of a number and its reciprocal is$2\frac{1}{6}$. $2\frac{1}{6}$ can be converted into the fraction form as follows,

=>$2\frac{1}{6}$ = (6x2+1)/6 = 13/6.

3. The sum of the number and its reciprocal is 13/6. Mathematically the statement can also be written as,

=> x + (1/x) = 13/6,

4. Solve the above equation for the value of x,

=>$\frac{x^2+1}{x} = \frac{13}{6}$,

=>$6*(x^2+1) = 13x,$

=>$6x^2 - 13x + 6 = 0,$

=> $(3x-2)(2x-3) = 0,$

=> x = 3/2 or x = 2/3.

5. The equation is satisfied for two values of x, 2/3, and 3/2.

Therefore, the values of x are 2/3 and 3/2.