Question

biet : bz-cy/a = cx-az/b= ay-bx/c 

CMR : x/a=y/b=z/c

Answer 1

cái này mà là toán lớp 7 á

Answer 2

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

\(\Rightarrow\frac{a\left(bz-cy\right)}{a^2}=\frac{b\left(cx-az\right)}{b^2}=\frac{c\left(ay-bx\right)}{c^2}\)

\(\Rightarrow\frac{abz-acy}{a^2}=\frac{bcx-abz}{b^2}=\frac{acy-bcx}{c^2}=\frac{abz-acy+bcx-abz+acy-bcx}{a^2+b^2+c^2}\)

\(=\frac{0}{a^2+b^2+c^2}=0\)

\(\Rightarrow abz=acy\Rightarrow\frac{y}{b}=\frac{z}{c};bcx=abz\Rightarrow\frac{x}{a}=\frac{z}{c}\Rightarrow\frac{x}{a}=\frac{y}{b}=\frac{z}{c}\)