Question

Tìm x, y, z, thỏa mãn \(\frac{x+5}{4}=\frac{y-4}{3}=\frac{z-3}{2}\) và \(x+2y-3z=12\)

Answer 1

x=13; y=35/2; z=12. (t/m)

Chức bạn học tốt!!!

Answer 2

Ta có: \(\frac{x+5}{4}=\frac{y-4}{3}=\frac{z-3}{2}\)

\(\Rightarrow\frac{x+5}{4}=\frac{2\left(y-4\right)}{2.3}=\frac{3\left(z-3\right)}{3.2}\)

\(\Rightarrow\frac{x+5}{4}=\frac{2y-8}{6}=\frac{3z-9}{6}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{x+5}{4}=\frac{2y-8}{6}=\frac{3z-9}{6}=\frac{x+5+2y-8-3z+9}{4+6-6}=\frac{12+6}{4}=\frac{18}{4}\)

\(\left\{{}\begin{matrix}\frac{x+5}{4}=\frac{18}{4}\Rightarrow x+5=\frac{18}{4}.4=18\Rightarrow x=18-5=13\\\frac{2y-8}{6}=\frac{18}{4}\Rightarrow2y-8=\frac{18}{4}.6=27\Rightarrow2y=27+8=35\Rightarrow y=\frac{35}{2}\\\frac{3z-9}{6}=\frac{18}{4}\Rightarrow3z-9=\frac{18}{4}.6=27\Rightarrow3z=27+9=36\Rightarrow z=36:3=12\end{matrix}\right.\)

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