Question 831629
{{{e^x-e^(-x)=1}}}
{{{e^(2x)-1=e^x}}}
{{{e^(2x)-e^x-1=0}}}
Let {{{u=e^x}}}, {{{u^2=e^(2x)}}},
{{{u^2-u-1=0}}}
{{{u = (-(-1) +- sqrt( (-1)^2-4*1*(-1) ))/(2*1) }}}
{{{u = (1 +- sqrt( 1+4 ))/(2) }}}
{{{u = (1 +- sqrt(5 ))/(2) }}}
Only the positive solution works in this case since {{{e^x>0}}}
{{{e^x=(1+sqrt(5))/2}}}
{{{highlight_green(x=ln(1+sqrt(5))/2)}}}
{{{ graph( 300, 300, -2, 2, -2, 2, e^x-e^(-x)) }}}