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1.5a Lösning 6b - Versionshistorik
2026-11-05T17:12:05Z
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Taifun den 14 juli 2014 kl. 19.14
2014-07-14T19:14:59Z
<p></p>
<p><b>Ny sida</b></p><div><math>\begin{align} {1+x \over 1} & = {1 \over x} \qquad\qquad | \, \cdot x{\color{White} x} \\<br />
x \cdot (1 + x) & = 1 \\<br />
x + x^2 & = 1 \qquad\qquad | \, -1 \\<br />
x^2 + x - 1 & = 0 \\<br />
x_{1,2} & = -{1 \over 2} \pm \sqrt{{1 \over 4} + 1} \\<br />
x_{1,2} & = -{1 \over 2} \pm \sqrt{5 \over 4} \\<br />
x_1 & = -{1 \over 2} + {1 \over 2} \cdot \sqrt{5}={1 \over 2}\,(-1 + \sqrt{5})={\sqrt{5}-1 \over 2} = 0,618033989\cdots \\<br />
x_2 & = -{1 \over 2} - {1 \over 2} \cdot \sqrt{5}=-{1 \over 2}\,(1 + \sqrt{5})=-\,{1+\sqrt{5} \over 2}\; {\rm :negativ} \\<br />
g & = {\sqrt{5}-1 \over 2} \approx 0,618033989<br />
\end{align}</math></div>
Taifun