Đáp án:
Giải thích các bước giải:
Từ `\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=0`
`⇔\frac{ayz+bxz+cxy}{xyz}=0⇔ayz+bxz+cxy=0`
`⇔\frac{ayz+bxz+cxy}{abc}=0⇔\frac{yz}{bc}+\frac{xz}{ac}+\frac{xy}{ab}=0`
Ta có: `\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}`
`=[\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}+2(\frac{yz}{bc}+\frac{xz}{ac}+\frac{xy}{ab})]-2(\frac{yz}{bc}+\frac{xz}{ac}+\frac{xy}{ab})`
`=(\frac{x}{a}+\frac{y}{b}+\frac{z}{c})^2-2.0=1^2-0=1(đpcm)`