Question

[Hoàng Minh]

dùng K nha mấy bạn

Answer 1

[ILoveMath]

1. Áp dụng t/c dtsbn ta có:

\(\dfrac{x}{1}=\dfrac{y}{6}=\dfrac{z}{3}=\dfrac{2x-3y+4z}{2.1-3.6+4.3}=\dfrac{24}{-4}=-6\)

\(\dfrac{x}{1}=-6\Rightarrow x=-6\\ \dfrac{y}{6}=-6\Rightarrow y=-36\\ \dfrac{z}{3}=-6\Rightarrow z=-18\)

2. Áp dụng t/c dtsbn ta có:

\(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}=\dfrac{\left(5z-25\right)-\left(3x-3\right)-\left(4y+12\right)}{5.6-3.2-4.4}=\dfrac{5z-3x-4y-25+3-12}{8}=\dfrac{50-25+3-12}{8}=\dfrac{16}{8}=2\)

\(\dfrac{x-1}{2}=2\Rightarrow x=5\\ \dfrac{y+3}{4}=2\Rightarrow z=5\\ \dfrac{z-5}{6}=2\Rightarrow z=17\)

3.\(6x=10y=15z\Rightarrow\dfrac{x}{\dfrac{1}{6}}=\dfrac{y}{\dfrac{1}{10}}=\dfrac{z}{\dfrac{1}{15}}\)

Áp dụng t/c dtsbn ta có:

\(\dfrac{x}{\dfrac{1}{6}}=\dfrac{y}{\dfrac{1}{10}}=\dfrac{z}{\dfrac{1}{15}}=\dfrac{x+y-z}{\dfrac{1}{6}+\dfrac{1}{10}-\dfrac{1}{15}}=\dfrac{90}{\dfrac{1}{5}}=450\)

\(\dfrac{x}{\dfrac{1}{6}}=450\Rightarrow x=75\\ \dfrac{y}{\dfrac{1}{10}}=450\Rightarrow y=45\\ \dfrac{z}{\dfrac{1}{15}}=450\Rightarrow z=30\)

Answer 2

[Hoàng Minh]

Dùng K nha MN