Answer
Answer: $-26$ and $-24$ or $24$ and $26$.
Work Step by Step
Let the first even integer to be $x$
The consecutive second even integer is $x + 2$
i.e. $x^2+(x+2)^2=1252$
$\Rightarrow x^2+x^2+4x+4=1252$
$\Rightarrow 2x^2+4x-1248=0$
$\Rightarrow x^2+2x-624=0$
$\Rightarrow (x+26)(x-24)=0$
$\Rightarrow x=-26\hspace{0.3cm} or \hspace{0.3cm}x=24$
For $x=-26$, the second integer is $x + 2 = -26 + 2 = -24$
For $x=24$, the second integer is $x + 2 = 24 + 2 = 26$
Answer: $-26$ and $-24$ or $24$ and $26$.
