Question

Answer 1

Vì \(\left(x_1a-y_1b\right)^{2n}\ge0;...;\left(x_ma-y_mb\right)^{2n}\ge0\)

\(\Rightarrow VT\ge0\)

Mà  \(VT\le0\Rightarrow VT=0\Rightarrow\left\{{}\begin{matrix}x_1a-y_1b=0\\...\\x_ma-y_mb=0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x_1a=y_1b\\...\\x_ma=y_mb\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\dfrac{x_1}{y_1}=\dfrac{b}{a}\\...\\\dfrac{x_m}{y_m}=\dfrac{b}{a}\end{matrix}\right.\)

Áp dụng tc dtsbn:

\(\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}=...=\dfrac{x_m}{y_m}=\dfrac{x_1+x_2+...+x_m}{y_1+y_2+...+y_m}=\dfrac{b}{a}\left(đpcm\right)\)