Question

The product of two consecutive positive even integers is 168. What are the two integers?

Answer 1

12, 14

Explanation:

`n,\ n+2-\text{two consecutive positive even integers}\\\\(n)(n+2)-\text{their product}\\\\168-\text{their product}\\\\\text{The equation:}\\\\n(n+2)=168\qquad\text{use the distributive property}:\ a(b+c)=ab+ac\\\\(n)(n)+(n)(2)=168\\\\n^2+2n=168\qquad\text{add 1 to both sides}\\\\n^2+2n+1=168+1\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\n^2+2(n)(1)+1^2=169\\\\(n+1)^2=169\iff n+1=\pm√(169)\\\\n+1=\pm13\qquad\text{subtract 1 from both sides}\\\\n+1-1=-13-1\ \vee\ n+1-1=13-1\\\\n=-14<0\ \vee\ n=12`

`n+2=12+2=14`