Answer:
The two consecutive positive integers are 7 and 8
Step-by-step explanation:
Let
x ----> the first positive integer
x+1 ----> the second consecutive positive integer
we know that
[tex]x^{2} -17=4(x+1)[/tex]
Solve for x
[tex]x^{2} -17=4x+4\\ \\x^{2}-4x-21=0[/tex]
Solve the quadratic equation by graphing
The solution is x=7
see the attached figure
Find the value of x+1
x+1=7+1=8
therefore
The two consecutive positive integers are 7 and 8
