Question

What is the largest of three consecutive positive integers if the product of the two smallest is equal to 10 more than 4 times the largest?

Please explain and show full work.

Answer 1

let
x-----> the first positive integer
x+1---> the second positive integer
x+2---> the third positive integer

we know that
x*(x+1)=10+4*(x+2)
x²+x=10+4x+8
x²+x=18+4x
x²-3x-18=0

using a graph tool----> to resolve the second order equation
see the attached figure

the solution is
x=6
so
the numbers are
x=6
x+1=7
x+2=8

the answer is
the numbers are
6
7
and 8