Question 122437
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If the first even integer is n, the second is n + 2, and the third is n + 4.


We are given that {{{(n+4)^2=(n+2)^2+76}}}


Expand the binomials, collect terms, and solve for n


{{{(n+4)^2=(n+2)^2+76}}}
{{{n^2+8n+16=n^2+4n+4+76}}}
{{{8n-4n=4+76-16}}}
{{{4n=64}}}
{{{n=16}}}


So the first even integer is 16, the second is 18, and the third is 20.


<hr/>
<i>Check the answer</i>

{{{20^2=400}}}


{{{18^2=324}}} and {{{324+76=400}}}





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