Question 178286
Call the consecutive even integers
{{{n}}}, {{{n + 2}}}, and {{{n+4}}}
given:
{{{(n + 4)^2 = (n + 2)^2 + 100}}}
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{{{n^2 + 8n + 16 = n^2 + 4n + 4 + 100}}}
{{{4n = 104 - 16}}}
{{{4n = 88}}}
{{{n = 22}}}
{{{n + 2 = 24}}}
{{{n + 4 = 26}}}
The numbers are 22,24, and 26
check:
{{{(n + 4)^2 = (n + 2)^2 + 100}}}
{{{26^2 = 24^2 + 100}}}
{{{676 = 576 + 100}}}
{{{676 = 676}}}
OK