SOLUTION: the sum of the squares of two consecutive even integers is 52. what are the integers? I believe the answers is 4^2 and 6^2 but I can't figure out how to write an equation to show

Question 148437: the sum of the squares of two consecutive even integers is 52. what are the integers? I believe the answers is 4^2 and 6^2 but I can't figure out how to write an equation to show how I figured it out, Please help!!!
Found 2 solutions by edjones, Earlsdon:
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Let the smaller be x, the larger x+2
x^2+(x+2)^2=52
x^2+x^2+4x+4=52
2x^2+4x-48=0
2(x^2+2x-24)=0
(x+6)(x-4)=0
x=4
x+2=6
.
Ed
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Try this!
Let x be the first even integer, then (x+2) is the next consecutive even integer.
The sum of their squares is expressed by:
and this is equal to 52, so you can write the equation:
Simply this.
Combine like-terms and subtract 52 from both sides.
Now you have a quadratic equation that can be solved by factoring after dividing through by 2 to simplify it a bit.
Factor.
from which you get:
or
The integers are 4 and 6 or -6 and -4
Check:
= or...
=

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