Question 623326
I can say {{{ z = w^2 }}} and
{{{ w^4 - 20w^2 - 2 = z^2 - 20z - 2 }}}
{{{ z^2 - 20z - 2 = 0 }}}
Use quadratic formula
{{{ z = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = -20 }}}
{{{ c = -2 }}}
{{{ z = (-(-20) +- sqrt( (-20)^2 - 4*1*(-2) )) / (2*1) }}}
{{{ z = ( 20 +- sqrt( 400 + 8)) / 2 }}}
{{{ z = ( 20 +- 20.199) / 2 }}}
{{{ z = 40.199/2 }}}
{{{ z = 20.0995 }}}
and
{{{ z = -.199/2 }}}
{{{ z = -.0995 }}}
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{{{ z = w^2 }}}
{{{ w = sqrt(z) }}}
{{{ w = sqrt( 20.0995 )  }}} 
{{{ w = 4.4832 }}}
and
{{{ w = sqrt( -.0995 ) }}}
{{{ w = .3154i }}}
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check answer:
{{{ w^4 - 20w^2 - 2 = 0 }}}
{{{ .3154^4* i^4 - 20*.3154^2 * i^2 - 2 = 0 }}}
{{{ .009896 * 1 - 1.9895 * (-1) - 2 = 0 }}}
{{{ .009896 + 1.9895 - 2 = 0 }}}
{{{ 1.9994 - 2 = 0 }}}
{{{ .00056 = 0 }}}
error due to rounding off?
You can check other answer