Question

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

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

Answer 1

Lời giải:

Áp dụng TCDTSBN:

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

$=\frac{bza-cya}{a^2}=\frac{cxb-azb}{b^2}=\frac{ayc-bxc}{c^2}$

$=\frac{bza-cya+cxb-azb+ayc-bxc}{a^2+b^2+c^2}=\frac{0}{a^2+b^2+c^2}=0$

$\Rightarrow bz-cy=cx-az=ay-bx$

$\Rightarrow \frac{a}{x}=\frac{b}{y}=\frac{c}{z}$

Hay $a:b:c=x:y:z$ (đpcm)