Question 178836
Call the smallest interger {{{n}}}
The next larger even integer is {{{n + 2}}}
The next larger even integer is {{{n + 4}}}
The next larger even integer is {{{n + 6}}}
given:
{{{n(n+2) = (n+4)(n+6) - 56}}}
{{{n^2 + 2n = n^2 + 10n + 24 - 56}}}
{{{8n = 56 - 24}}}
{{{8n = 32}}}
{{{n = 4}}}
{{{n+2 = 6}}}
{{{n+4 = 8}}}
{{{n+6 = 10}}}
The numbers are 4,6,8,and 10
check:
{{{n(n+2) = (n+4)(n+6) - 56}}}
{{{4(4+2) = (4+4)(4+6) - 56}}}
{{{4*6 = 8*10 - 56}}}
{{{24 = 24}}}
OK