8th grade homework

Question

The sum of a number and its reciprocal is 13/6. Find the number.

Answer 1

n = number

1 / n = its reciprocal

 

n + 1/n = 13/6           Multiply all by n

n² + 1 = 13n/6           Multiply all by 6

6n² + 6 = 13n

6n² - 13n + 6 = 0

(6n - 1)(n - 6) = 0

{6, 1/6}

 

The number is 6 and the reciprocal is 1/6.    Or

The number is 1/6 and the reciprocal is 6.