Annahme 1 (Bestätigt)

[latex]g^* = \frac{1}{\varphi ^2}[/latex]

[latex]\frac{3-\sqrt{5}}{2} = \frac{1}{(\frac{1+\sqrt{5}}{2})^2}[/latex]

[latex]\frac{3-\sqrt{5}}{2} = \frac{1}{\frac{(1+\sqrt{5})^2}{2^2}}[/latex]

[latex]\frac{3-\sqrt{5}}{2} = \frac{4}{(1+\sqrt{5})^2}[/latex]

[latex]3-\sqrt{5} = \frac{8}{(1+\sqrt{5})^2}[/latex]

[latex]3-\sqrt{5} = \frac{8}{1 + 2\sqrt{5} + 5}[/latex]

[latex]3-\sqrt{5} = \frac{8}{6 + 2\sqrt{5}}[/latex]

[latex]3-\sqrt{5} = \frac{8}{2 (3 + \sqrt{5})}[/latex]

[latex]3-\sqrt{5} = \frac{4}{3 + \sqrt{5}}[/latex]

[latex](3-\sqrt{5})(3 + \sqrt{5}) = 4[/latex]

[latex]3^2 - 5 = 4[/latex]

[latex]9 - 5 = 4[/latex]

[latex]4 = 4[/latex] wzbw.

Dadurch resultieren einige Dinge wie z.B.

[latex]\varphi^2 + g^* = \varphi^2 + \frac{1}{\varphi ^2} = 3[/latex]


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