Question

tìm x,y,z biết

a, / 2x + 5/ + / 2x - 3 / = 8

b, \(\dfrac{2x-y}{5}=\dfrac{3y-2z}{15}\)và x+z=2y

Answer 1

a) Ta có: \(\left|2x+5\right|+\left|2x-3\right|=8\)

\(\Rightarrow\left|2x+5\right|+\left|3-2x\right|=8\)

Nhận thấy \(\left[{}\begin{matrix}\left|2x+5\right|\ge2x+5\forall x\\\left|3-2x\right|\ge3-2x\forall x\end{matrix}\right.\)

\(\Rightarrow\left|2x+5\right|+\left|3-2x\right|\ge2x+5+3-2x\forall x\)

\(\Rightarrow\left|2x+5\right|+\left|3-2x\right|\ge8\)

Dấu \("="\) xảy ra khi \(\left[{}\begin{matrix}2x+5\ge0\\3-2x\ge0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x\ge-5\\2x\le3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x\ge\dfrac{-5}{2}\\x\le\dfrac{3}{2}\end{matrix}\right.\) \(\Rightarrow\dfrac{-5}{2}\le x\le\dfrac{3}{2}\)

Vậy \(\dfrac{-5}{2}\le x\le\dfrac{3}{2}.\)