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

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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)   (Show Source): You can put this solution on YOUR website!
Let the number be x and its' reciprocal be 

1. x +  =   --- Our equation

2. x^2 + 1 =    ---  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 =  or 3  --- Our answer.

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

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