Question

Bài 1: tìm x , y , z biết

\(\dfrac{x+1}{111}=\dfrac{y+2}{222}=\dfrac{z+4}{333}\) và 3x + 2y + z =989

Bài 2: Cho x - y = 1.Tìm GTNN của A biết:

A= 3x - 2y + | 2x - y + 2017 |

Answer 1

\(\dfrac{x+1}{111}=\dfrac{y+2}{222}=\dfrac{z+4}{333}\\ \Leftrightarrow\dfrac{3\left(x+1\right)}{3\cdot111}=\dfrac{2\left(y+2\right)}{2\cdot222}=\dfrac{z+4}{333}\\ \Leftrightarrow\dfrac{3x+3}{333}=\dfrac{2y+4}{444}=\dfrac{z+4}{333}\)

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

\(\dfrac{3x+3}{333}=\dfrac{2y+4}{444}=\dfrac{z+4}{333}=\dfrac{3x+3+2y+4+z+4}{333+444+333}=\dfrac{3x+2y+z+11}{1110}=\dfrac{999+11}{1110}=\dfrac{1110}{1110}=1\\ \Rightarrow\left\{{}\begin{matrix}\dfrac{3x+3}{333}=1\Rightarrow3x+3=333\Rightarrow3x=330\Rightarrow x=110\\\dfrac{2y+4}{444}=1\Rightarrow2y+4=444\Rightarrow2y=440\Rightarrow y=220\\\dfrac{z+4}{333}=1\Rightarrow z+4=333\Rightarrow z=329\end{matrix}\right.\)

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Answer 2

\(\dfrac{x+1}{111}=\dfrac{y+2}{222}=\dfrac{z+4}{333}\)

\(\Rightarrow\dfrac{3x+3}{333}=\dfrac{2y+4}{444}=\dfrac{z+4}{333}\)

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

\(\dfrac{3x+3}{333}=\dfrac{2y+4}{444}=\dfrac{z+4}{333}=\dfrac{3x+3+2y+4+z+4}{333+444+333}=\dfrac{1000}{1110}=\dfrac{100}{111}\)Thay vào tính