Question

The sum of the number and its reciprocal is 34/15. What is the number

Answer 1

Answer:

3/5 or 5/3

Step-by-step explanation:

let the number be x

it's reciprocal will be 1/x

sum of the two is 34/15

$x + \frac{1}{x} = \frac{34}{15} \\ \frac{ {x}^{2} + 1 }{x} = \frac{34}{15} \\ 15( {x}^{2} + 1) = 34 \times x \\ 15 {x}^{2} + 15 = 34x \\ 15 {x}^{2} - 34x + 15 = 0 \\ 15 {x}^{2} - 25x - 9x + 15 = 0 \\ 5x(3x - 5) - 3(3x - 5) = 0 \\ (5x - 3)(3x - 5) = 0 \\ 5x - 3 = 0 \: \: \: \: \: \: 3x - 5 = 0 \\ x = \frac{3}{5} \: \: \: \: \: \: \: \: x = \frac{5}{3}$