Question 1102396
{{{ 2*log( x ) = -log( 6 - x^2 ) }}}
{{{ log( x^2 ) = log( ( 6 - x^2 )^(-1) ) }}}
{{{ x^2 = 1/( 6 - x^2 ) }}}
{{{ 6x^2 - x^4 = 1 }}}
---------------------------
Let {{{ x^2 = z }}}
{{{ z^2 - 6z + 1 = 0 }}}
Use quadratic formula
{{{ z = ( -b +-sqrt( b^2 - 4*a*c ))/(2a) }}}
{{{ a = 1 }}}
{{{ b = -6 }}}
{{{ c = 1 }}}
{{{ z = ( 6 +-sqrt( 36 - 4 ) ) / 2 }}}
{{{ z = ( 6 + sqrt( 32 ) ) / 2 }}}
{{{ z = ( 6 + 4*sqrt(2) ) / 2 }}}
{{{ z =  3 + 2*sqrt(2)  }}}
and
{{{ z = 3 - 2*sqrt(2) }}}
----------------------------
{{{ z = x^2 }}}
{{{ x = sqrt(z) }}}
----------------------------
{{{ x = sqrt( 3 + 2*sqrt(2) ) }}}
{{{ x = -sqrt( 3 + 2*sqrt(2) ) }}}
{{{ x = sqrt( 3 - 2*sqrt(2) ) }}}
{{{ x = -sqrt( 3 - 2*sqrt(2) ) }}}
----------------------------
Get a 2nd opinion if needed