SOLUTION: using the five step method .the sum of a number and its reciprocal is 10/3.what is the number? please show step one through 5. thanks

Algebra ->  Matrices-and-determiminant -> SOLUTION: using the five step method .the sum of a number and its reciprocal is 10/3.what is the number? please show step one through 5. thanks      Log On


   

Question 48440: using the five step method .the sum of a number and its reciprocal is 10/3.what is the number? please show step one through 5. thanks
Answer by atif.muhammad(135) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number be x and its' reciprocal be 1%2Fx

1. x + 1%2Fx = 10%2F3  --- Our equation

2. x^2 + 1 = 10x%2F3   ---  Form the equation around a common denominator

3. 3x^2 - 10 x + 3 = 0 --- Re-arrange the equation

4. (3x-1)(x-3) = 0 --- Factorise the quadratic

5. x = 1%2F3 or 3  --- Our answer.

 (The two possible answers are both reciprocals of each other)