Question 31323
you had an error with your signs half way through...


{{{ 4x^-4-16x^-2+4=0 }}}
{{{ 4/x^4-16/x^2+4=0 }}}
{{{ 4-16x^2+4x^4=0 }}}
{{{ 4x^4-16x^2+4=0 }}}
{{{ x^4-4x^2+1=0 }}}


this doesn't factorise simply. So lets use the quadratic formula.


First however, let {{{y=x^2}}} --> {{{ y^2-4y+1=0 }}}


so, {{{ y = (-b +- sqrt(b^2 - 4ac))/(2a) }}}
{{{ y = (-(-4) +- sqrt((-4)^2 - 4(1)(1)))/(2(1)) }}}
{{{ y = (4 +- sqrt(16 - 4))/(2) }}}
{{{ y = (4 +- sqrt(12))/(2) }}}
{{{ y = (4 +- sqrt(4*3))/(2) }}}
{{{ y = (4 +- sqrt(4)sqrt(3))/(2) }}}
{{{ y = (4 +- 2sqrt(3))/(2) }}}
{{{ y = (2(2 +- sqrt(3)))/(2) }}}
{{{ y = 2 +- sqrt(3) }}}


so, {{{ y = 2 + sqrt(3) }}} or {{{ y = 2 - sqrt(3) }}}


Hence, from {{{y=x^2}}}, we get:
{{{ x = sqrt(2 + sqrt(3)) }}} or {{{ x = -sqrt(2 + sqrt(3)) }}}
{{{ x = sqrt(2 - sqrt(3)) }}} or {{{ x = -sqrt(2 - sqrt(3)) }}}


jon.