[tex]\frac{a}{x}+\frac{b}{y}+\frac{c}{z} = 0 <=> ayz+bxz+cxy=0 \\ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 <=> (\frac{x}{a}+\frac{y}{b}+\frac{z}{c})^{2}=1 \\ => \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}} + 2(\frac{x}{ab}+\frac{yx}{bc}+\frac{zx}{ca})=1 \\ <=> \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}} = 1- 2(\frac{x}{ab}+\frac{yx}{bc}+\frac{zx}{ca}) = 1 - 2 \frac{ayz+bxz+cxy}{abc} = 1-2.0 = 1[/tex]
=> Đpcm