cho (bz-cy):a=(cx-az):b=(ay-bx):c
chứng minh x:a=y:b=z:c
cho (bz-cy):a=(cx-az):b=(ay-bx):c
chứng minh x:a=y:b=z:c
Learn from yesterday, live for today, hope for tomorrow. The important thing is not to stop questioning -Albert Einstein-
$\frac{bz-cy}{a}=\frac{cx-az}{b}=\frac{ay-bx}{c}$
$=\frac{a(bz-cy)}{a^{2}}=\frac{b(cx-az)}{b^{2}}=\frac{c(ay-bx)}{c^{2}}$
$=\frac{abz-acy}{a^{2}}=\frac{bcx-abz}{c^{2}}=\frac{acy-bcx}{c^{2}}$
$=\frac{abz-acy+bcx-abz+acy-bcx}{a^{2}+b^{2}+c^{2}}=0$
$\Rightarrow \frac{bz-cy}{a}=0 \Rightarrow bz-cy=0 \Rightarrow bz=cy \Rightarrow \frac{z}{c}=\frac{y}{b}$ (1)
$\Rightarrow \frac{cx-az}{b}=0 \Rightarrow cx-az=0 \Rightarrow cx=az \Rightarrow \frac{x}{a}=\frac{z}{c}$ (2)
Từ (1) và (2) => đpcm
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