Question 1093358
Let the facing pages be {{{ n }}} and {{{ n+1 }}}
given:
{{{ n*( n+1 ) = 7140 }}}
{{{ n^2 + n = 7140 }}}
complete the square
{{{ n^2 + n + (1/2)^2 = 7140 + (1/2)^2 }}}
{{{ ( n + 1/2 )^2 = 28560/4 + 1/4 }}}
{{{ ( n + 1/2 )^2 = 28561/4 }}}
{{{ ( n + 1/2 )^2 = ( 169/2 )^2 }}}
Take the square root of both sides
{{{ n + 1/2 = 169/2 }}}
{{{ n = 168/2 }}}
{{{ n = 84 }}}
and
{{{ n+1 = 85 }}}
The facing pages are 84 and 85
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check:
{{{ n*( n+1 ) = 7140 }}}
{{{ 84*85 = 7140 }}}
{{{ 7140 = 7140 }}}
OK