Find the sum of the reciprocals of two real numbers, given that these two numbers have a sum of 50 and a product of 25.

Source: mathcontest.olemiss.edu 5/7/2007

**SOLUTION**

The above figure shows the graph of the line and the graph of the hyperbola . The two intersection points of the two graphs are two symmetrical points and . The sum of the reciprocals is

.

An alternative way to find the sum of the reciprocals without knowing the values of is:

**Answer**: 2.

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Retired high school math teacher.