Problem:
Let a,b, and c be three distinct one-digit numbers. What is the maximum value of the sum of the roots of the equation (x−a)(x−b)+(x−b)(x−c)=0 ?
Answer Choices:
A. 15
B. 15.5
C. 16
D. 16.5
E. 17
Solution:
If (x−a)(x−b)+(x−b)(x−c)=0, then (x−b)(2x−(a+c))=0, so the two roots are b and 2a+c​. The maximum value of their sum is 9+28+7​=16.5​.
The problems on this page are the property of the MAA's American Mathematics Competitions