Question 992383
Let the consecutive even integers =
{{{ n }}}, {{{ n+2 }}}, and {{{ n + 4 }}}
given:
{{{ n^2 + ( n+2 )^2 = 2*( n+4 ) }}}
{{{ n^2 + n^2 + 4n + 4 = 2n + 8 }}}
{{{ 2n^2 + 2n- 4 = 0 }}}
{{{ n^2 + n - 2 = 0 }}}
{{{ ( n + 2 )*( n - 1 ) = 0 }}}
{{{ n = -2 }}} ( ignore the positive root )
{{{ n + 2 = 0 }}}
{{{ n + 4 = 2 }}}
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The consecutive even integers are:
-2, 0, and 2
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check:
{{{ n^2 + ( n+2 )^2 = 2*( n+4 ) }}}
{{{ (-2)^2 + ( -2+2 )^2 = 2*( -2+4 ) }}}
{{{ 4 + 0 = 2*2 }}}
{{{ 4 = 4 }}}
OK