[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]
