Answer:
-4 and -2
2 and 4.
Step-by-step explanation:
Let n be the first even integer.
Then the consecutive even integer will be represented by (n+2).
We know that their product is 8. So:
[tex]n(n+2)=8[/tex]
Solve for n. Distribute:
[tex]n^2+2n=8[/tex]
Subtract 8 from both sides:
[tex]n^2+2n-8=0[/tex]
Factor:
[tex](n+4)(n-2)=0[/tex]
Zero Product Property
[tex]n+4=0\text{ or } n-2=0[/tex]
Solve for n for each case:
[tex]n=-4\text{ or } n=2[/tex]
Hence, we will have two correct solutions.
Case 1: -4 and -2. -4(-2) is indeed 8.
Case 2: 2 and 4. 2(4) is also 8.
Hence, our solutions are:
-4 and -2
2 and 4.
