Đặt $\left\{\begin{matrix}
\dfrac{a_1}{a_2}=p & \\
\dfrac{b_1}{b_2}=q & \\
\dfrac{c_1}{c_2}=r &
\end{matrix}\right.$
$→ \left\{\begin{matrix}
p+q+r=0 \quad (1) & \\
\dfrac{1}{p}+\dfrac{1}{q}+\dfrac{1}{r}=1 \quad (2) & \\
\end{matrix}\right.$
Từ $(2)→\dfrac{1}{p^2}+\dfrac{1}{q^2}+\dfrac{1}{r^2}+2\dfrac{p+q+r}{pqr}=1$
Kết hợp vời $(1)→\dfrac{1}{p^2}+\dfrac{1}{q^2}+\dfrac{1}{r^2}=1$
$→$ $\dfrac{a_2^2}{a_1^2}+\dfrac{b_2^2}{b_1^2}+\dfrac{c_2^2}{c_1^2}=1$