The sum of a number and its reciprocal is 50/7. Find the number. List all possible solutions. The answers must be reduced fractions or integers.

Question

The sum of a number and its reciprocal is 50/7. Find the number.

List all possible solutions. The answers must be reduced fractions or integers.

Answer 1

Let x = the number

1/x = its reciprocal

x + 1/x = 50/7

(x² +1)/x = 50/7

7x² + 7 = 50x

7x² - 50x +7 = 0

Using Quadratic formula:

x = (50±√((-50)² - 4•7•7))/14

x= (50±√(2500 - 196)/14

x= (50±√(2304)/14

x= (50±48)/14

x₁ = 1/7

x₂ = 7