Cho \(\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}=\frac{ay-2bx}{3c}\) . Chứng minh : \(\frac{x}{a}=\frac{y}{2b}=\frac{z}{3c}\)
Cho \(\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}=\frac{ay-2bx}{3c}\).Chứng minh rằng : \(\frac{x}{a}=\frac{y}{2b}=\frac{z}{3c}\)
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Cho dãy số : \(\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}=\frac{ay-2bx}{3c}\)
Chứng minh : \(\frac{x}{a}=\frac{y}{2b}=\frac{z}{3c}\)
\(\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}=\frac{ay-2bx}{3c}\)
Suy ra: \(\frac{a.\left(2bz-3cy\right)}{a.a}=\frac{2b\left(3cx-az\right)}{2b.2b}=\frac{3c.\left(ay-2bx\right)}{3c.3c}\)
\(\Rightarrow\frac{2abz-3acy}{a^2}=\frac{3bcx-abz}{2b^2}=\frac{acy-2cbx}{3c^2}\)
Theo tính chất dãy tỉ số bằng nhau
\(\frac{2abz-3acy+6bcx-2abz+3acy-6bcx}{a^2+2b^2+3c^2}=\frac{0}{a^2+2b^2+3c^2}=0\)
\(\Rightarrow\hept{\begin{cases}2bz=3cy\\3cx=az\\ay=2bx\end{cases}\Rightarrow\hept{\begin{cases}\frac{z}{3c}=\frac{y}{2b}\\\frac{x}{a}=\frac{z}{3c}\\\frac{y}{2b}=\frac{x}{a}\end{cases}}\Rightarrow\frac{x}{a}=\frac{y}{2b}=\frac{z}{3c}}\)
=> đpcm
Cho dãy tỉ số bằng nhau\(\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}=\frac{ay-2bx}{3c}\)Chứng minh \(\frac{x}{a}=\frac{y}{2b}=\frac{z}{3c}\)
cho dãy tỉ số bằng nhau: \(\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}=\frac{ay-2bx}{3c}\)
chứng minh \(\frac{x}{a}=\frac{y}{2b}=\frac{z}{3c}\)
Với a,b,c khác 0, cho dãy tỉ số bằng nhau\(\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}=\frac{ay-2bx}{3c}\).Chứng minh:\(\frac{x}{a}=\frac{y}{2b}=\frac{z}{3c}\)
Cho dãy tỉ số bằng nhau \(\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}=\frac{ay-2bx}{3c}\)
Chứng minh rằng \(\frac{x}{a}=\frac{y}{2b}=\frac{z}{3c}\)
Cho dãy tỉ số bằng nhau:\(\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}=\frac{ay-2bx}{3c}\)
Chứng mính:\(\frac{x}{a}=\frac{y}{2b}=\frac{z}{3c}\)
Theo đề: \(\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}=\frac{ay-2bx}{3c}\)
\(\Rightarrow\frac{2bza-3acy}{a^2}=\frac{6cxb-2bza}{4b^2}=\frac{3ayc-6bxc}{9c^2}\)
\(=\frac{2bza-3cya+6xbc-2bza+3ayc-6bxc}{a^2+4b^2+9c^2}\)
\(=0\)
\(\Rightarrow\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}=\frac{ay-2bx}{3c}=0\)
\(\Rightarrow2bz=3cy;3cx=az;ay=2bx\)
\(\Rightarrow\frac{x}{a}=\frac{y}{2b}=\frac{z}{3c}\left(đpcm\right)\)
Ta có: \(\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}=\frac{ay-2bx}{3c}\)
\(\Rightarrow\frac{2bzx-3cyx}{ax}=\frac{3cxy-azy}{2by}=\frac{ayz-2bxz}{3xz}\)
\(=\frac{2bzx-3cyx-3cxy-azy-ayz-2bxz}{ax-2by-3xz}=0\)
\(\Rightarrow\)\(\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}=\frac{ay-2bx}{3c}=0\)
\(\Rightarrow2bz=3cy;\)\(3cx=az;\)\(ay=2bx\)
\(\Rightarrow\frac{x}{a}=\frac{y}{2b}=\frac{z}{3c}\).
Cho \(\frac{2bz-3cy}{a}\text{=}\frac{3cx-az}{2b}\text{=}\frac{ay-2bx}{3c}\)
Chứng minh : \(\frac{x}{a}\text{=}\frac{y}{2b}\text{=}\frac{z}{3c}\)
Cho \(\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}=\frac{ay-2bx}{3c}\)
CMR:\(\frac{x}{a}=\frac{y}{2b}=\frac{z}{3c}\)
Từ\(\frac{2bz-3cy}{a}=\frac{3cx-az}{2b}\Rightarrow4b^2z-6bcy=3acx-a^2z\)
\(\Rightarrow\)\(\left(4b^2+a^2\right)z=3c\left(ax+2by\right)\)
\(\Rightarrow\frac{z}{3c}=\frac{ax+2by}{a^2+4b^2}=\frac{ax}{a^2}=\frac{2by}{4b^2}\Rightarrow\frac{z}{3c}=\frac{x}{a}=\frac{y}{2b}\)