Question

Biết \(\dfrac{bz-cy}{a}=\dfrac{cx-az}{b}=\dfrac{ay-bx}{c}\)

Chứng minh rằng \(\dfrac{x}{a}=\dfrac{y}{b}=\dfrac{z}{c}\)

Answer 1

\(\dfrac{bz-cy}{a}=\dfrac{cx-az}{b}=\dfrac{ay-bx}{c}=\dfrac{abz-acy}{a^2}=\dfrac{bcx-baz}{b^2}=\dfrac{cay-cbz}{c^2}=\dfrac{abz-acy+bcx-baz+cay-cbx}{a^2+b^2+c^2}\)

\(\Rightarrow\dfrac{bz-cy}{a}=0\)

\(\Rightarrow bz-cy=0\)

\(\Rightarrow bz=cy\Rightarrow\dfrac{b}{y}=\dfrac{c}{z}\)

tương tự \(\dfrac{c}{z}=\dfrac{a}{x}\)

Vậy \(\dfrac{a}{x}=\dfrac{b}{y}=\dfrac{c}{z}\left(đpcm\right)\)

Answer 2

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