Question

\(\frac{x-1}{2}\) = \(\frac{y+3}{4}\) = \(\frac{z-5}{6}\) và 5x-3y-4z=46

tìm x, y, z

Answer 1

Ta có:

\(\frac{5x-5}{10}=\frac{3y+9}{12}=\frac{4z-20}{24}\)

Áp dụng t/c dãy tsbn:

\(\frac{5x-5}{10}=\frac{3y+9}{12}=\frac{4z-20}{24}=\frac{5x-5-3y-9-4z+20}{10-12-24}\)

\(=\frac{\left(5x-3y-4z\right)+6}{-26}=\frac{52}{-26}=-2\)

\(\Leftrightarrow\left\{{}\begin{matrix}\frac{x-1}{2}=-2\\\frac{y+3}{4}=-2\\\frac{z-5}{6}=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-1=-4\\y+3=-8\\z-5=-12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\\y=-11\\z=-7\end{matrix}\right.\)

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