Question

two sets of 3 consecutive integers have a property that the product of the larger two is one less than seven times the smallest set up and solve an equation that can be used to find both sets of intigers

Answer 1

Answer:
First set is 3,4 and 5
Second set is 1,2 and 3

Step-by-step explanation:
Assume that the smallest number is n.
Since the three numbers are consecutive, this means that the other two numbers would be n+1 and n+2

Now, we know that the product of the larger two numbers is 1 less tan than 7 times the smallest.
This means that:
(n+1)(n+2) = 7n - 1 .........> equation used to find the sets
n² + 2n + n + 2 = 7n - 1
n² + 3n + 2 = 7n - 1
n² + 3n + 2 - 7n + 1 = 0
n² - 4n + 3 = 0
(n-3)(n-1) = 0
This means that:
either n-3=0 ..........> n = 3
or n-1=0 ..........> n = 1

At n = 3:
The three numbers would be 3,4 and 5

At n = 1:
The three numbers would be 1,2 and 3

Hope this helps :)