1966 AHSME Problems/Problem 3
Revision as of 09:28, 2 April 2008 by 1=2 (talk | contribs) (New page: ==Problem== If the arithmetic mean of two numbers is <math>6</math> and their geometric mean is <math>10</math>, then an equation with the given two numbers as roots is...)
Problem
If the arithmetic mean of two numbers is and their geometric mean is , then an equation with the given two numbers as roots is:
Solution
Let the numbers be and .
.
.
The monic quadratic with roots and is . Therefore, an equation with and as roots is