Number Problem 15 Solution

A number added to five times its reciprocal is -6. Find the number.



Solution to the problem:




A number = x

Reciprocal of that number would be 1/x

5 times the reciprocal would be  5 *  1/x   =  5/x

A number added to five times its reciprocal would then be x + 5/x

This then is equal to -6.

x + 5/x = = -6

Multiply by x...

x^2 + 5 = -6x

x^2 + 6x + 5 = 0

(x + 1 )(x + 5 )

The answer are -1 and -5.


Check

-1 + 5/-1  = -1 -5 = -6  Correct and

-5 + 5/-5 = -5 -1 = -6  Correct