Answer :
Since an even number can be represented as:
[tex]2n[/tex]With n a natural number, and the next even number is:
[tex]2n+2[/tex]Set the sum of both even numbers equal to 126:
[tex](2n)+(2n+2)=126[/tex]Solve for n:
[tex]\begin{gathered} \Rightarrow2n+2n+2=126 \\ \Rightarrow4n+2=126 \\ \Rightarrow4n=126-2 \\ \Rightarrow4n=124 \\ \Rightarrow n=\frac{124}{4} \\ \Rightarrow n=31 \end{gathered}[/tex]Substitute back n=31 into the expressions for the even numbers to find them:
[tex]\begin{gathered} 2(31)=62 \\ 2(31)+2=64 \end{gathered}[/tex]Therefore, the two consecutive even numbers whose sum is 126, are 62 and 64.