Question 1128224
Let the roots be {{{ r[1] }}} and {{{ r[2] }}}
{{{ ( x - r[1] )*( x - r[2] ) = x^2 - ( r[1] + r[2] )*x + r[1]*r[2] }}}
{{{ 2x^2 - 2k*x +  4 = 0  }}}
{{{ x^2 - k*x + 2 = 0 }}}
{{{ k = r[1] + r[2] }}}
{{{ r[1]*r[2] = 2 }}}
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Let {{{ r[2] = sqrt(3) - 1 }}}
{{{ r[1] = k - r[2] }}}
{{{ r[1] = k - sqrt(3) - 1 }}}
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{{{ r[1]*r[2] = 2 }}}
{{{ ( -sqrt(3) + ( k-1 ) )*( sqrt(3) - 1 ) = 2 }}}
{{{ -3 + ( k-1 )*sqrt(3) + sqrt(3) - ( k-1 ) = 2 }}}
{{{ -3 + k*sqrt(3) - sqrt(3) + sqrt(3) - k + 1 = 2 }}}
{{{ k*sqrt(3) - k = 4 }}}
{{{ k*( sqrt(3) - 1 ) = 4 }}}
{{{ k = 4/( sqrt(3) - 1 ) }}}
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get another opinion, too. This is hard to prove.