Đáp án:
1
Giải thích các bước giải:
\(\begin{array}{l}
\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1\\
\Rightarrow {(\frac{x}{a} + \frac{y}{b} + \frac{z}{c})^2} = 1\\
\Leftrightarrow \frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} + \frac{{2xy}}{{ab}} + \frac{{2yz}}{{bc}} + \frac{{2xz}}{{ac}} = 1\\
\Leftrightarrow \frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} + \frac{{2(xyc + yza + xzb)}}{{abc}} = 1\\
\frac{a}{x} + \frac{b}{y} + \frac{c}{z} = 0\\
\Leftrightarrow \frac{{yza + xzb + xyc}}{{xyz}} = 0\\
\Rightarrow yza + xzb + xyc = 0\\
\Rightarrow \frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} + \frac{0}{{abc}} = 1\\
\Rightarrow \frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} = 1
\end{array}\)
