Let x be the middle of three consecutive integers. The squares of the largest integer x+1 must be 25 more than the product of the other two integers x-1 and x. Setting up the equation (x+1)2 - 25 = x(x-1) and solving for x yields x = 8. Therefore, the three consecutive integers are 7, 8, 9.

1. Find three consecutive integers such that the square of the largest number is 25 more than the
product of the other two.
a.) define the varaible e.g Let x= the number of coins
b.) State the equation necessary to solve the problem
c.) Solve equation
show all work
Solution
Let x be the middle number. So, the other two numbers are (x-1) and (x+1)
According to the question,
(x+1) 2 -25 = x(x-1)
x 2
+ 1 + 2x - 25 = x 2
- x
=> 2x - 24 = -x
=> 3x = 24
=> x = 8
Hence, the three consecutive integers are : 7,8,9