Junior Math League Competition
Subject:
Algebra [1]
The following are the 2 problems from the NVCM math league contest. The answers will be provided at the bottom.
Note: This requires knowledge and use of both geometry and algebra. Also " means the same as the previous equation.
1. The difference between two consecutive perfect squares is 739. Write the larger of these perfect squares.
Solution:
Let x^2 be the larger and (x-1)^2 be the smaller of the two squares. Then
739= x^2-(x-1)^2
"=x^2-(x^2-2x+1)
"=2x-1
740=2x
370=x
You must find the larger which is represented by x^2 so----
x^2
370^2
136,900---- Answer
2. The product of two positive, consecutive odd integers is 4623. Find the smaller integer.
Solution: