![](bestanden/q12553img1.gif)
Er geldt:
$
\eqalign{
& z^2 + z^2 = \left( {2\left( {z - 1} \right)} \right)^2 \cr
& 2z^2 = 4\left( {z - 1} \right)^2 \cr
& 2z^2 = 4z^2 - 8z + 4 \cr
& z^2 - 4z + 2 = 0 \cr
& (z - 2)^2 - 2 = 0 \cr
& z = 2 - \sqrt 2 \,\,\left( {v.n.} \right) \vee z = 2 + \sqrt 2 \cr}
$
Of:
$
\eqalign{
& z\sqrt 2 = z - 1 + z - 1 \cr
& z\sqrt 2 = 2z - 2 \cr
& 2z - z\sqrt 2 = 2 \cr
& z(2 - \sqrt 2 ) = 2 \cr
& z = \frac{2}
{{2 - \sqrt 2 }} = 2 + \sqrt 2 \cr}
$
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