[Toán 8]Biến đổi đồng nhất

C

congchuaanhsang

$\dfrac{a}{x}+\dfrac{b}{y}+\dfrac{c}{z}$=0 \Leftrightarrow $ayz+bxz+cxy=0$

$( \dfrac{x}{a}+\dfrac{y}{b}+\dfrac{z}{c} )^2$=1

\Leftrightarrow$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}+2(\dfrac{xy}{ab}+\dfrac{yz}{bc} + \dfrac{xz}{ac} )$=1

\Leftrightarrow$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}+\dfrac{2(ayz+bxz+cxy)}{abc}$=1

Mà $ayz+bxz+cxy=0$\Rightarrow$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}=1$
 
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