Answer:
The numbers are 23 and 24
Step-by-step explanation:
Let
x ----> the first positive consecutive integer
x+1 ----> the second positive consecutive integer
we know that
The product of the two consecutive positive integers is 552
so
The algebraic expression that represent this situation is
[tex]x(x+1)=552[/tex]
Convert to expanded form
[tex]x^2+x-552=0[/tex]
Solve the quadratic equation by graphing
The roots of the equation are
[tex]x_1=-24[/tex] ----> the number cannot be negative
[tex]x_2=23[/tex]
see the attached figure
therefore
[tex]x=23\\x+1=24[/tex]
The numbers are 23 and 24
