Answer:
9
Step-by-step explanation:
Let the three consecutive positive integers be:
If the product of the two smaller integers is 2 more than 8 times the largest integer then:
[tex]\implies x(x+1)=8(x+2)+2[/tex]
Solve the equation for x:
[tex]\implies x^2+x=8x+16+2[/tex]
[tex]\implies x^2+x=8x+18[/tex]
[tex]\implies x^2-7x-18=0[/tex]
[tex]\implies x^2-9x+2x-18=0[/tex]
[tex]\implies x(x-9)+2(x-9)=0[/tex]
[tex]\implies (x+2)(x-9)=0[/tex]
Therefore:
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies x-9=0 \implies x=9[/tex]
As x is a positive integer, x = 9.
