Question

[bui]

giai giup minh nhe

Answer 1

[Đào Anh Phương]

\(7x=3y\Rightarrow\frac{x}{3}=\frac{y}{7}\)

\(5y=7z\text{ }\Rightarrow\text{ }\frac{y}{7}=\frac{z}{5}\)

\(\Rightarrow\frac{x}{3}=\frac{y}{7}=\frac{z}{5}=\frac{xy}{3y}=\frac{yz}{7z}=\frac{zx}{5x}\)

Áp dụng tính chất dãy tỉ số bằng nhau và xy + xz - yz = 4 ta có

\(\frac{xy}{3y}=\frac{yz}{7z}=\frac{zx}{5x}=\frac{xy+xz-yz}{3y+5x-7z}=\frac{4}{3y+5x-7z}\)

\(=\frac{x}{3}=\frac{y}{7}=\frac{z}{5}=\frac{5x}{15}=\frac{3y}{21}=\frac{7z}{35}=\frac{3y+5x-7z}{15+21-35}=3y+5x-7z\)

+) Có: \(\frac{4}{3y+5x-7z}=3y+5x-7z\text{ }\Rightarrow\text{ }\left(3y+5x-7z\right)^2=4\text{ }\Rightarrow\orbr{\begin{cases}3y+5x-7z=2\\3y+5x-7z=-2\end{cases}}\)

TH1: 3y + 5x - 7z = 2

\(\Rightarrow\frac{x}{3}=\frac{y}{7}=\frac{z}{5}=2\)

\(\Rightarrow\hept{\begin{cases}x=6\\y=14\\z=10\end{cases}}\)

TH2: 3y + 5x - 7z = -2

\(\Rightarrow\frac{x}{3}=\frac{y}{7}=\frac{z}{5}=-2\text{ }\Rightarrow\hept{\begin{cases}x=-6\\y=-14\\z=-10\end{cases}}\)

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