Question 580366
Let the numbers be {{{ a }}} and {{{ b }}}
{{{ a + b = 77 }}}
{{{ a*b = 1440 }}}
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{{{ b = 77 - a }}}
and
{{{  a*( 77 - a ) = 1440 }}}
{{{ 77a - a^2 = 1440 }}}
{{{ a^2 - 77a + 1440 = 0 }}}
Use quadratic formula
{{{ x = (-b +- sqrt( b^2-4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = -77 }}}
{{{ c = 1440 }}}
{{{ x = (-(-77) +- sqrt( (-77)^2-4*1*1440 )) / (2*1) }}}
{{{ x = ( 77 +- sqrt( 5929 - 5760 )) / 2 }}}
{{{ x = ( 77 +- sqrt( 169 )) / 2 }}}
{{{ x = ( 77 +- 13) / 2 }}}
{{{ x = 90/2 }}}
{{{ x = 45 }}}
and
{{{ x = 64/2 }}}
{{{ x = 32 }}}
{{{ a + b = 77 }}}
{{{ 45 + 32 = 77 }}}
{{{ 77 = 77 }}}
The numbers are 32 and 45
check:
{{{ a*b = 1440 }}}
{{{ 32*45 = 1440 }}}
OK