Solve the number problem.

Question

The sum of a number and its reciprocal is 29/10. Find the number and its reciprocal. 

 

Smaller value = 

 

Larger value =

Answer 1

Let x be the unknown number.  Its reciprocal is 1/x.

 

x + 1/x = 29/10

 

Multiply both sides by 10x to get rid of the denominators:

 

10x² + 10 = 29x

10x² - 29x + 10 = 0

 

Solve for x by factoring (it does factor) or by using the quadratic formula.  You'll get two answers which are reciprocals of one another.