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JULIAZTE3ON
Rozwiązane

uzasadnij że jesli [tex]\frac{a}{b} = \frac{b}{c} \\[/tex]
to [tex]\frac{a^{2} +b^{2} }{b^{2} +c^{2} } =\frac{a}{c}[/tex]

Odpowiedź :

ZBIORJON

[tex]Jesli:~~\dfrac{a}{b} =\dfrac{b}{c} ~~\Rightarrow ~~b^{2} =ac\\\\\\Teza~~do~~udowodnienia: \dfrac{a^{2} +b^{2} }{b^{2} +c^{2} } =\dfrac{a}{c} \\\\Dowod:\\\\L=\dfrac{a^{2} +b^{2} }{b^{2} +c^{2} }=\dfrac{a^{2} +ac }{ac+c^{2} }=\dfrac{a\cdot (a+c)}{c\cdot (a+c)} =\dfrac{a}{c} \\\\P=\dfrac{a}{c} \\\\L=P ~~cbdu[/tex]

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