matematikk.net

(Beklager utydelig bilde. Hvis noe er uklart kan jeg skrive det opp.)


Jeg har klart alt frem til 6.51 e).
Her har jeg stilt opp proposjonen [tex]\frac{AC}{AD} = \frac{AE}{AC}[/tex]
eller [tex]AC^2 = AD \cdot AE[/tex].
Jeg skal sltså bevise at [tex]AC^2 + BC^2 = AB^2[/tex]
Men hva skal jeg gjøre nå?

du har jo at [tex]\,\,AC^2\,=\,AE\cdot AD\,=\,b^2[/tex]

og fra tegninga blir AD = c - a og AE = c + a
slik at:

[tex]b^2\,=\,(c+a)(c-a)\,=\,c^2\,-\,a^2[/tex]

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*facepalm*