Question 148437
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:
{{{x^2+(x+2)^2}}} and this is equal to 52, so you can write the equation:
{{{x^2+(x+2)^2 = 52}}} Simply this.
{{{x^2+(x^2+4x+4) = 52}}} Combine like-terms and subtract 52 from both sides.
{{{2x^2+4x-48 = 0}}} Now you have a quadratic equation that can be solved by factoring after dividing through by 2 to simplify it a bit.
{{{x^2+2x-24 = 0}}} Factor.
{{{(x-4)(x+6) = 0}}} from which you get:
{{{x = 4}}} or {{{x = -6}}}
The integers are 4 and 6 or -6 and -4
Check:
{{{4^2+6^2= 16+36}}}={{{52}}} or...
{{{(-6)^2+(-4)^2 = 36+16}}}={{{52}}}