Question 600262
Let the 3 consecutive positive integers =
{{{ n }}}
{{{ n + 1 }}}
{{{ n + 2 }}}
given:
{{{ n*( n + 1 ) = ( n + 1 )*( n + 2 ) - 26 }}}
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{{{ n^2 + n = n^2 + 3n + 2 - 26 }}}
Subtract {{{ n^2 }}} from both sides
{{{ n = 3n + 2 - 26 }}}
{{{ n = 3n - 24 }}}
{{{ 2n = 24 }}}
{{{ n = 12 }}}
{{{ n + 1 = 13 }}}
{{{ n + 2 = 14 }}}
The 3 consecutive positive integers are 12, 13, and 14
check:
{{{ n*( n + 1 ) = ( n + 1 )*( n + 2 ) - 26 }}}
{{{ 12*13 = 13*14 - 26 }}}
{{{ 156 = 182 - 26 }}}
{{{ 156 = 156 }}}
OK