Tìm x, y, z biết x/3 = y/2 và 2x^3 + 3y^3 = 7

\(\dfrac{x}{3}=\dfrac{y}{2};\dfrac{x}{4}=\dfrac{z}{5}\) và \(x+y-z=10\)

Ta có:

\(\dfrac{x}{3}=\dfrac{y}{2}\Leftrightarrow\dfrac{x}{12}=\dfrac{y}{8};\dfrac{x}{4}=\dfrac{z}{5}\Leftrightarrow\dfrac{x}{12}=\dfrac{z}{15}\)

\(\Rightarrow\dfrac{y}{8}=\dfrac{x}{12}=\dfrac{z}{15}\) và \(x+y-z=10\)

AD tính chất DTS bằng nhau ta có:

\(\dfrac{y}{8}=\dfrac{x}{12}=\dfrac{z}{15}=\dfrac{x+y-z}{12+8-15}=\dfrac{10}{5}=2\)

+) \(\dfrac{y}{8}=2\Rightarrow y=16\)

+) \(\dfrac{x}{12}=2\Rightarrow x=42\)

+) \(\dfrac{z}{15}=2\Rightarrow z=30\)

Vậy \(x=42;y=16;z=30\)

c,\(\dfrac{x}{2}=\dfrac{y}{5};\dfrac{y}{3}=\dfrac{z}{2}\) và \(2x+3y-4z=34\)

Ta có:

\(\dfrac{x}{2}=\dfrac{y}{5}\Leftrightarrow\dfrac{x}{6}=\dfrac{y}{15};\dfrac{y}{3}=\dfrac{z}{2}\Leftrightarrow\dfrac{y}{15}=\dfrac{z}{10}\)

\(\Rightarrow\dfrac{x}{6}=\dfrac{y}{15}=\dfrac{z}{10}\)

Ta lại có:

\(\dfrac{2x}{12}=\dfrac{3y}{45}=\dfrac{4z}{40}\) và \(2x+3y-4z=34\)

AD tính chất DTS bằng nhau ta có:

\(\dfrac{2x}{12}=\dfrac{3y}{45}=\dfrac{4z}{40}=\dfrac{2x+3y-4z}{12+45-40}=\dfrac{34}{17}=2\)

+) \(\dfrac{2x}{12}=2\Rightarrow x=12\)

+) \(\dfrac{3y}{45}=2\Rightarrow y=30\)

+) \(\dfrac{4z}{40}=2\Rightarrow z=20\)

Vậy \(x=12;y=30;z=20\)

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